Pellegrini's men moved into the quarter-finals of the FA Cup with an accomplished performance against their Premier League title rivals, who had completed a league double against City with a 1-0 win at the Etihad Stadium 12 days earlier.
Stevan Jovetic put City ahead after 16 minutes, before Samir Nasri sealed the triumph in the second half with a goal in his first appearance since suffering a knee injury last month.
The Chilean had been embroiled in a war of words with Chelsea boss Jose Mourinho in the build-up to the game but, despite City's fine display, Pellegrini denied suggestions his side had sent a message to the Stamford Bridge outfit and their other Premier League challengers with the performance.
"The way we won today is important for the trust of the team," Pellegrini said. "It's important for continuing in FA Cup, but nothing more."
City's midweek home clash with Sunderland was postponed due to high winds, while Chelsea played out a 1-1 draw at West Brom on Tuesday.
And - after disappointing showings in league games against Chelsea and Norwich City - Pellegrini was quick to highlight the extra rest as a factor in City's dominant victory.
"It was very important for our team not to play against Sunderland on Wednesday," Pellegrini added.
"This team has played 18 games in the last two months and I saw that the team was not fresh, that's why we were a little down in our performances against Chelsea (in the league) and against Norwich.
"But working on Thursday and Friday I saw that the team was fresh and was absolutely sure that we were going to have a very good game as we did."
