They got knocked out but they got up again. For José Mourinho's Real Madrid, the latest clásico was always likely to be less about the result and more about recovery after a week of intrigue and insult. As Pep Guardiola insisted on the eve of the game, Barcelona had a problem: the assumption was that the Catalans were already in the semi-final. A place in the next round was not really at stake; instead the prize was something less tangible. This morning, it is Barcelona who are through but Madrid emerged from a wonderful 2-2 draw as winners too.

Suddenly, unexpected, deservedly, a semi-final slot had been within Madrid's reach. In the end they could not grab it but they did grab a lifeline. Madrid never expected to progress in the cup but the progression was evident. Mourinho's side have now faced Barcelona 10 times and won just once. The run was extended but it felt like it had been ended. Mourinho underlined the comment going round the away dressing room: "it's impossible to win here." Yet the lasting impression was the exact opposite: it no longer looks impossible to win here. Barely 24 hours earlier, it did.

Barcelona, admitted both Catalan football dailies, Sport and El Mundo Deportivo, had confronted the "best Madrid". Barça had got through "by the hairs" – the skin of their teeth. Fortune had not favoured the team that, this time at least, chose to be brave. Madrid had competed for possession and for territory. They also had more shots. Barcelona fans revealed a banner before the game. A spoof advert, copied from the one with which Real Madrid fans taunted Atlético Madrid supporters, it mocked: "Wanted: a worthy rival for a decent clásico." This was a more than decent clásico and it was a more than decent Madrid. Sport called it a clash of the titans. El País had seen "the best Madrid and the worst Barcelona".

Sergio Ramos declared himself "super proud" of his team. They had been, he said, "very superior". "We leave with the feeling that today we have stood up to them," said Iker Casillas. "We feel like we played well and that we deserved much more. We played well; we gave them hardly any opportunities and we depart proud and happy of our team. This is the way we have to carry on. Playing like this, we can achieve a lot."

Casillas also admitted that he had confronted the referee in the tunnel, telling him: "Now go and party with Barcelona." It was, he said, a moment's rush of blood, quickly forgotten. Alvaro Arbeloa did not forget so fast. "We got as far as they would let us," he said. At El Prat airport, Madrid fans waited for their team with protest chants of "Hands up! This is a robbery!"

The refereeing was a useful shield behind which some could hide, and Marca called the official "horrible". But it was not necessary for Madrid to hide. What mattered was that their fans had been there to greet them at all. From villains to heroes. "Barcelona went through, Madrid came back," said the cover of AS, while Marca's cover ran on: "They had it … Barcelona knock out a Madrid side that were, for the first time, very much the better team."

Beyond the result, that matters. AS's resident mad Madridista Tomás Roncero emerged from his depression. "Today more than ever before I am proud to be a Madrid fan," he wrote. "This is what we wanted from Mourinho and he responded perfectly. Madrid do not fear anyone because their sacred badge keeps on winning games with its mere presence. Madrid fans know that it's in their hands now: the league and the Champions League. With football like this no one will show them a lack of respect again. Madrid justify the meaning of life. ETERNAL REAL. I love you."

The key word was "today". The fact that Madrid had approached the game in a manner so radically different from the first leg and been far closer to winning was not lost on many. The inevitable response was: "Why didn't you do that before?!" Mourinho said he had "not learned a lesson" at the Camp Nou, but most saw a lesson in this result: Barcelona can be attacked. If you try to attack them. Alfredo Relaño, so critical of Mourinho of late, blamed the knockout on poor finishing and Madrid's "cowardly" approach in the first leg. "Yes, you can," he said. "With the good players on the pitch."

"Madrid's charge was savage and beautiful, like the British Light Brigade," wrote Santi Giménez. "They fell with honour, but they fell – thanks to the bad orders that came from General Mourinho. He was Lord Raglan, who from his comfortable position at General HQ sent his men out to a certain death, massacred in the valley of death. Madrid were never closer [to beating Barcelona]. With a better performance in the first game, this draw would have tasted like victory." Late last night, it did.