City won 2-0 after having captain Vincent Kompany sent off after just 10 minutes.
Pellegrini said: "I think it was a very good response from the team. It was a very difficult week and then we had to start this game playing with one player less after 10 minutes.
"It was more difficult to play with 10 players but I trust the team, I trust the players and I think we did really well with the ball."
On Kompany's dismissal, he added: "I thought before it was clear foul by (Nikica) Jelavic - before Vincent did his foul - but the referee didn't see it, he saw the foul of Kompany and he sent him off."
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