Pellegrini came in for criticism after last week's 1-0 loss to the Londoners, the feeling being he was tactically outgunned.
But the Chilean vowed to stick to his methods and that was vindicated as Chelsea struggled to impose themselves in the game.
Pellegrini even felt the potentially damaging loss, as well as a goalless draw at Norwich, had jolted his side into action.
He said: "We saw again the team that was playing before the last two games.
"It was very important for us to lose three points in the Premier League against a very good team with great players.
"The way we won today is important for the trust of the team, for continuing in the FA Cup. For our team it is a very important competition also, but nothing more."
The result kept alive City's challenge in four competitions but Pellegrini is not interested in discussing a potential quadruple.
He said: "We never talk about that. We try to fight in all the competitions as far we can.
"It is one step more but we continue now in Champions League."
Barcelona visit Eastlands for the first leg of their last-16 tie on Tuesday.
Pellegrini said: "We will start thinking about Barcelona tomorrow.
"Here it was very important to have the performance we did in all senses - defending, possession, attacking.
"Chelsea didn't have any chances to shoot at our goal. That is important for the trust of the individuals."
His captain Vincent Kompany openly said that it was great to have "revenge" over the Blues, but Pellegrini took a quite different view of events.
Pellegrini said: "No, it was not revenge. We didn't want to lose two games against Chelsea here at home.
"The team played very well in all senses.
"It was very important for our team not to play against Sunderland, as this team played 18 games in the last two months and we were not fresh.
"That is why we were a little down in our performance against Chelsea and Norwich but working again on Thursday and Friday I saw the team was fresh and I was absolutely sure we were going to have a very good game."