José Mourinho claimed Chelsea were back "among the best eight clubs in the world" after last season's Europa League winners eased beyond Galatasaray to ensure there will be at least one English team participating in a Champions League quarter-final this season.

The Portuguese said he hopes his side will be joined on Wednesday by Manchester United, who are seeking to overturn a 2-0 deficit from the first leg against Olympiakos, but praised his players for outclassing their Turkish opposition to force passage into the next round. Mourinho has never lost a quarter-final tie in the Champions League and will await Friday's draw for the last eight in Nyon with relish after beating Galatasaray 2-0 on the night and 3-1 on aggregate.

"We are there [in the last eight] but it's different from last season because, then, that was the Europa League and at a different level," he said. "To come from the Europa League to the quarter-finals of the Champions League is important for the club, important for the players. We are a Champions League club and now we are among the best eight, the best clubs in the world, and we are there. The players deserve to be there.

"All the big teams are there. All the big candidates to win the competition are there. And we would welcome any one of them. It would be very good for our evolution as a team and very important for us to play one of the best. We wait for the draw. It doesn't matter who. They are all welcome." The manager suggested he had been unaware of his own record in the last eight of Europe's elite competition. "Why should other teams fear [Chelsea]? I've never lost in a quarter-final? I've never thought about it."

Mourinho, who had watched from afar as the London club failed to make it out of the group stage in the Champions League despite being holders last season, is expected to be charged with misconduct by the Football Association on Wednesday and fined around £10,000 after being sent to the stands for encroaching on the pitch in Saturday's defeat at Aston Villa. It was the second time this season that he has been dismissed from his technical area after a misdemeanour in October's victory over Cardiff, an offence which prompted a standard £8,000 fine.

Tuesday night's occasion was considerably more comfortable than the match at Villa Park, with Didier Drogba – granted a rapturous reception before kick-off and a fine send-off at the end on his first appearance at Stamford Bridge since leaving Chelsea in 2012 – becalmed by the excellent John Terry and Gary Cahill. The veteran was presented with a silver boot to mark his eight-year spell at Chelsea but was granted only one glimpse of goal, and that came in second-half stoppage time.

"The most difficult thing was the way his team played," said Mourinho. "When you are a striker, if your team doesn't produce attacking football, you feel like a lonely man. It happens to every striker in the world: if the team is not there to play behind you, you are a lone[ly] man. So I think he couldn't do much. I have to say, in my opinion, Gary and John made a fantastic performance against two very good strikers in Burat [Yilmaz] and Didier. But the fact is we controlled the game so well that you could never see Didier in dangerous positions."

The Galatasaray manager, Roberto Mancini, was disgusted with his side's display. "We prepared this game and started at 1-1," the Italian said. "I was confident we'd do a good game, have chances to score, but it was really important to start the game without conceding a goal. Instead we conceded after four minutes [to Samuel Eto'o]. During the game our more experienced players did nothing. For this reason it's difficult for me. We didn't have any players who 'played' this game. We can't play like we did in this performance [and expect to do well]. If we want to play at this level, we need to work more and do more steps [forward]."

The former Manchester City manager's parting shot was to tip his former club to pip Chelsea for the Premier League title. "I think that Manchester City are the best team," he said. "They are the best team. They have the best players. I think that Manchester City have a big chance to win the Premier League, probably against Chelsea. I don't know if Liverpool, who are doing very well at this moment, can win it. I think it will be a fight until the end with Chelsea."

Chelsea renew their challenge by hosting Arsenal on Saturday lunchtime in Arsène Wenger's 1,000 match in charge of their London rivals. Mourinho confirmed the home side would not be making a pre-match presentation to the visiting manager to mark the occasion. "No, because the best present is to have 1,000 matches in the same club," he said. "If Chelsea gives me the chance to arrive to 1,000 matches, I'd be the happiest man there is in the world."