The Premier League leaders sealed a 4-0 aggregate win against Borussia Moenchengladbach in Budapest on Tuesday after a 2-0 victory in the second leg, courtesy of goals from Kevin De Bruyne and Ilkay Gundogan.
The Champions League is the one major prize that has eluded Guardiola since he arrived at the Etihad in 2016.
“Since the first year I arrived they told me that you have to win the Champions League,” said the City boss, who won Europe’s elite club competition twice as Barcelona manager.
“It is always on our shoulders but I’m not concerned about that. If you deserve it in football, you go through. If you don’t, you don’t.”
City, who have never been crowned European champions, are chasing an unprecedented quadruple in the current campaign.
They look almost certain to win a third Premier League title in four seasons, face Everton in the FA Cup quarter-finals on Saturday and play Tottenham in the final of the League Cup in April.
“I’m more than incredibly impressed and delighted for our players in this tough year for everyone in society,” said Guardiola.
“Being 14 points clear in the Premier League, in the final of the League Cup, quarter-final of the Champions League and going to play to get to the semi-finals of the FA Cup.
“This is more than winning one quarter-final or one last-16 game. It means that in nine to 10 months, every three days, you are there — and this is the best title you can get.
“Of course for the prestige for all of us, because we are here to win like all other clubs, we have to try in the end to lift some titles,” added the 50-year-old Catalan.
City already had one foot in the last eight before they returned to the Hungarian capital to complete the job they started against Moenchengladbach at the same venue three weeks ago.
Early strikes from De Bruyne and Gundogan put the match beyond the reach of the Bundesliga club. The matches were moved to Budapest because of coronavirus travel restrictions.
