Following back-to-back losses to Aston Villa and Bayern Munich, the Chilean's charges triumphed 3-1 over Everton on Saturday to move into the Premier League's top four
Pellegrini's side fell behind to an early goal from Romelu Lukaku, but strikes from Alvaro Negredo, Sergio Aguero and an own goal from Tim Howard turned the game in City's favour.
The win came following consecutive defeats against Aston Villa and Bayern Munich, and Pellegrini was quick to express satisfaction at how his side responded to those setbacks.
When asked what impressed him about his team's display, Pellegrini told BT Sport: "The character of the team.
"It was not easy today to play against the only unbeaten team in the Premier League. It was not an easy game after what happened on Wednesday [against Bayern].
"The most important thing is the way you react, we reacted very, very well.
"We had at least four or five more chances to score, Everton didn't really have any other chances aside from the goal at the beginning."
City's away form has been disappointing so far this season, suffering defeats at Cardiff City and Aston Villa, while also dropping points at Stoke City.
And the Chilean is eager to atone for those disappointments after the upcoming international break, when City face trips to West Ham United and Chelsea.
"I think we have surrendered some points playing away," he added.
"When we come back from the international break we play two away games against West Ham and Chelsea, we must try to recover the points we have lost."