City came into the game having being defeated by Aston Villa and then European champions Bayern Munich in midweek.
But City bounced back and actually came from behind to seal a 3-1 win over Everton at the Etihad Stadium.
"I'm very pleased for a lot of things," Pellegrini smiled.
"We played the only unbeaten team in the league and they played very well with the ball so it wasn't an easy match.
"Last Wednesday had a mental and physical consequence, so I'm very pleased with the character we showed today."
Pellegrini also dismissed any claims that referee Jonathan Moss had an adverse effect on the game, despite the final goal coming via a controversially awarded penalty - which was actually missed but then deflected in by Tim Howard.
"I never talk about referees but I'm absolutely sure that the difference between Manchester City and Everton today was not the referee," he stated.
"I haven't seen the penalty incident yet - but that was not the difference today."
Pellegrini picked under-fire goalkeeper Joe Hart despite many papers claiming he could be set to drop him after a number of high-profile mistakes.
"It was not a simple decision to keep Joe Hart in the team but I know that he needs all of our trust - the trust of me, the players and the fans," he said.
"He has to play with England two games more and Joe is exactly the same as the other players, he showed great character today."