Following last week's pulsating 2-2 draw at the Parc des Princes, Kevin De Bruyne settled a tense affair 1-0 in City's favour with 14 minutes remaining at the Etihad Stadium on Tuesday.
The win means City move into the semi-finals of Europe's top competition for the first time, adding a further twist to a season where they have beaten Liverpool on penalties to lift the League Cup but faltered badly to fall out of the Premier League title race.
Pellegrini, who will make way for Pep Guardiola at the end of the campaign, understands the scrutiny attracted by City's lavish pursuit of success under owner Sheikh Mansour and is keen to push their Champions League run on towards May's final in Milan.
"It is one of the targets of this club to try and improve every year," hPellegrini said.
"I know we have received a lot of criticism for different reasons but I think that we are improving.
"It is not easy because you have very strong teams in Europe but I am sure that the target of this club is to win the Champions League.
"Of course [City could win it] this season or next season.
"If you are in the semi-final you know that you have to play against a very big team of Europe but playing in the way we did tonight - I think we played better than Paris Saint-Germain, who are a very strong team with very strong players
Pellegrini was reluctant to discuss the prospect of taking on his successor if Guardiola's Bayern Munich overcome Benfica on Wednesday, but he acknowledged it was important for his own standing in the game to push City significantly beyond their previous Champions League best of a last-16 berth.
"We won the Premier League in my first year [2013-14] and two League Cups, so it was important to demonstrate that this team can improve in Europe, especially because I had a good performance with another team before," Pellegrini said.
"To leave this club without arriving to a new stage, I think that was a very bad thing for me. So I am happy, of course."
