The Blues suffered the ignominy of becoming the first holders to exit the competition at the group stage last term, responding by winning the Europa League, but are now in the last eight after first-half goals from Samuel Eto'o and Gary Cahill sealed a 2-0 second-leg win.
"We are there (in the last eight) - but it's different from last season because last season was the Europa League at a different level," Mourinho said on ITV.
"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."
Prior to the last-16 draw, Mourinho expressed a preference to play Didier Drogba's Galatasaray, but he has no such wish for Friday's quarter-final draw.
There are intriguing sub-plots aplenty in possible last-eight ties with Barcelona, Real Madrid, Pep Guardiola's Bayern Munich and Atletico Madrid, while Mourinho has not yet ruled Manchester United out of contention as David Moyes' men bid to overturn a 2-0 first-leg deficit at Old Trafford when they tackle Olympiacos on Wednesday night.
Mourinho said: "All the big candidates to win the competition. Welcome to any one of them.
"We wait for the draw. It doesn't matter who."
Mourinho has twice won the Champions League, with Porto in 2004 and Inter Milan in 2010, but fell short with Chelsea during his memorable first spell.
Drogba helped deliver the trophy owner Roman Abramovich coveted most in May 2012, his final kick in Chelsea blue the decisive penalty in the shoot-out with Bayern Munich.
The Ivory Coast striker, scorer of 157 goals in 341 appearances for Chelsea, was a peripheral figure on his return to his old stomping ground after being presented with a silver boot by the Blues prior to kick-off.
"The most difficult thing was the way his team played," Mourinho said.
"When you are a striker, if your team doesn't produce attacking football you feel a lonely man.
"He couldn't do much. Gary and John (Terry) had a fantastic performance. We controlled the game so well that we could never see Didier in the dangerous positions.
"We got a positive result in the first leg and in the second leg we finished the job.
"The team was very, very solid, very confident and very much in control for the 90 minutes.
"The 2-0 kept the result alive till the end. But the way we played was very solid. We were very much in control.
"We had the best chances to score the third goal, so probably the result could be a little bit bigger, because we were really much better than Galatasaray."
Chelsea's immediate attention turns to Saturday's Premier League showdown with Arsenal, where Mourinho's leaders will hope to put the controversial loss at Aston Villa firmly in the past in Arsene Wenger's 1,000th game as Gunners boss.
Wenger was branded a "specialist in failure" by Mourinho last month, but the Portuguese would like to emulate the Frenchman's landmark achievement.
Mourinho said: "If Chelsea gives me the chance to arrive to 1,000 matches I'll be the happiest manager in the world."
Roberto Mancini's visiting team were a distant second best throughout.
The former Manchester City manager was unable to explain his side's performance and was critical of the display as his return to England ended in a limp loss.
"We did nothing on the pitch," the Italian said.
"This game was difficult and after we conceded the first goal it was more difficult.
"It doesn't change that we didn't play this game, we played really bad.
"We didn't deserve anything in this game. Chelsea played better than us."
Mancini absolved Drogba of blame and refused to use Chelsea's presentation as an excuse for his underwhelming performance.
The Italian said: "He didn't have any chances to score. If you don't get a chance it's difficult."
Mancini led Manchester City to the 2012 Premier League title and was asked his opinion on the current four-team title race.
"I think that Manchester City's the best team," Mancini added.
"They have the best players. I don't know if Liverpool, also doing very well in this moment, can win.
"I think it will be a fight till the end between City and Chelsea."