Interviews with Giorgos Karagounis used to linger on football. They might touch upon the free-kick he looped beyond Fabien Barthez as Panathinaikos punctured Manchester United in the Champions League at the turn of the millennium or the diving header that scuttled through Arsenal's David Seaman a year later to thrust them into the competition's last eight. But they would inevitably gravitate towards that gloriously giddy summer of 2004 when Greece, against all the odds, prevailed in Portugal.

These days there are grittier matters on which to dwell. Talk drifts off piste to economic downturn and financial crisis, to compatriots struggling to make ends meet or even feed their families, and the smouldering sense of national pride that spurred Karagounis and his team-mates at Euro 2012 to party-poop their section and conjure an evening in Gdansk last June when politics and sport mixed far too readily. "Beating Russia and getting into that quarter-final with Germany was a great achievement," he says. "In terms of what we were up against, it was almost up there with what we did in Portugal winning the competition. It was us against everything. We had a duty to put a smile on people's faces back home."

Karagounis is a cult figure at Fulham, a veteran who was secured as a no-risk free transfer last summer and turned 36 last month but whose streetwise industry and weighty experience are already cherished by those in the Hammersmith end. Back in Athens he is iconic. This is a midfielder who, during 14 years in the national side, has won a record 124 caps and remains talismanic to the team currently second in World Cup qualifying Group G. He was a key player in 2004 and captain in 2012, even if he was to miss the culmination of both European campaigns – the first glittering, the second defiant – through suspension. He has featured for Internazionale in Italy, Benfica in Portugal and now in the Premier League, his reputation established and respected across the continent.

Others may bury their heads in the sand over events in a distant homeland, content with life in a Thames-side flat with Chelsea's Juan Mata and Oscar as neighbours, and ignoring the politics Karagounis freely admits he finds impenetrable. But there is no living in a football bubble when you are idolised by those who are suffering in a debt-ridden country as it gasps through its sixth year of recession, a third of the population living below the poverty line. "I'm luckier than most in Greece but, when you see your friends with the smile wiped from their face, not having enough to provide for their families, to buy food from the supermarket … You can't live your life oblivious to that, knowing how they're struggling back home. It's there all the time. Nagging at you. There is no escaping.

"We all felt it ahead of the Euros last summer. There was a desperation for us to do well. We had to give people something positive to cling to: they wanted us to put a smile on their faces, which is why the victory over Russia, the joy of winning that last group match to qualify, was almost doubled. It was about doing something for Greece and making people happy back home. It drove us on, particularly when it felt everything was going against us even there. We had to play half the first game [against the co-hosts Poland] with 10 men. I was booked against Russia when it was a clear penalty against me, which cost me a place in the quarter-final. And every single game was an away match because Greek fans couldn't afford to travel. But, despite all that, we got into that quarter-final. We made people happy. That meant something to all of us."

It was Karagounis's goal that defeated the Russians and forced passage out of the group, even if the player himself had to be substituted with his mind frazzled by a booking from the Swedish referee, Jonas Eriksson, after protesting the non-award of that penalty. The caution, his second of the competition, would deny him involvement in a poignant quarter-final. Germany are effectively Greece's biggest creditor and the country blamed for the severity of the austerity measures choking everyday life after the European Union bailout. The German chancellor, Angela Merkel, was in the crowd that day, watching on like Karagounis.

"It was a loaded occasion. Politically, it was charged," he says. "When we went to the Euros we all had dream scenarios in our minds. Mine was that we would meet Germany, partly because we hadn't played them for such a long time but also because of the significance of that contest, given everything the fixture would mean. Which is why I'd reacted so badly to being booked against Russia. I was devastated and, if I'd stayed on the pitch, I might have been sent off. My mind had gone and I was on the verge of doing something silly … This is the national team, my national team, and we'd need our experienced players against Germany. Seeing us then go on to lose [4-2] … It's hard to take. I've won so many caps but I missed that game and the final in 2004 through suspension. They changed the rules after that tournament and wiped yellow cards off at the semi-final stage. I was the last one to miss out on the old system. Jinxed."

At least he had celebrated with his team-mates at the Estádio da Luz while the world gawped at Greece's achievement. Almost nine years on and the names hardly trip off the tongue outside the Hellenic republic. That was a team spearheaded by Angelos Charisteas's goals and reliant upon the grey-haired Antonios Nikopolidis' saves. Angelos Basinas and Theo Zagorakis, the captain, graced the Premier League, two of eight from that squad who have featured in the English top flight even if only Stelios Giannokopoulos, at Bolton, made a prolonged impact. Yet when thrust together, in front of a disbelieving audience, Otto Rehhagel's team achieved something remarkable which, even now, seems inconceivable.

This unfancied side, ranked 35 in the world, had arrived with a record of five defeats and a draw (with West Germany in 1980) in major finals. And yet, having qualified for their first tournament in a decade, they beat the hosts in the opening game – with Karagounis kickstarting the tournament in style – knocked out the holders, France, the Czechs in the semis and, back in Lisbon, Luiz Felipe Scolari's Portuguese again in the final – not bad for a team whose base, in Vila do Conde, had been limited at best.

"People spoke about our organisation on the pitch but off it there simply wasn't any," says Karagounis. "We were probably the only national team at that tournament with no facilities available to us. We were staying in a hotel around 40km outside Porto with no gym, so if someone wanted to go and work out they had to find one locally.

All the other teams were staying in swish places with amazing facilities to use.

"But there was a sense of unity in that team. We worked for each other, struggled for each other, brought the best out of each other. We were committed, a tight group, and that was the driving force. The whole squad felt like a family. It got us through. The only regret is they didn't take advantage of what we achieved back in Greece.

"Sure, there was a new respect for the national team. Previously, the attitude had been club football was more important, that players shouldn't risk injuring themselves playing for the national team but save themselves for competitions like the Champions League. That changed. But in terms of organisation and infrastructure, winning Euro 2004 didn't kickstart anything. We had the team but not the structure. If anything, it's worse now than it was, given the economic crisis. The expectations of the national team may have risen but Greek football, in terms of infrastructure, is worse than it was 10 years ago."

Even so, it would still be easy to pine for home. It is apparently 23 degrees in Athens while, outside in the bitter cold, an April sky of dismal grey is belching flurries of snow on Motspur Park. Yet Karagounis's swansong with Fulham has actually whetted his appetite. His second stint at Pana had been drifting towards divorce last summer. Martin Jol had lost Danny Murphy, Dickson Etuhu and, on the eve of the transfer deadline, Mousa Dembélé and needed bodies. The veteran's availability had been advertised on the internet, his bustling energy, even in the twilight of his career, surely ready-made for the Premier League. He will make his 19th top-flight appearance at Newcastle on Sunday – he managed only 21 in two years with Inter in his pomp – to suggest this has been a successful marriage of convenience.

There is frustration this is all happening so late on in his career. "The facilities, the setup, the lack of politics behind it all … I love it here," he says. "There's a simplicity to it all, and it's refreshing. Proper football. I don't think the years I spent in Italy were wasted, even if I didn't play that many games, but I did have a chance to come to England after that (in 2005) and, in hindsight, that I should probably have taken the opportunity. I went to Benfica instead and loved it there, and now I'm finally here. The motivation is still there. I'm enjoying life. This is what I do. This is what I've always done, and the fans acknowledge the work I'm putting in. It's not just been about the impact I've made. It's about the impact these last seven months have had on me. It's been a great experience."There remains the possibility his stay could extend into a second campaign, though for that to happen his family would have to join him in London and the club would have to seek to renew his short-term deal. "We'd need both to happen before we know where I'll be next season but I'm sure there'll be talks, one way or the other.Wherever I am," he says, "I still want to play on and, ideally, get to the World Cup in Brazil. To take my country there would be the cherry on the cake. The perfect way to go out."