Man City had to do it the hard way against Hull after Vincent Kompany was shown a red card in only the 10th minute, but David Silva's exquisite strike three minutes later gave them a lead to protect.
Edin Dzeko added a late second as Man City moved back up to second place, providing Pellegrini with something to smile about after a week in which they were knocked out of the FA Cup and UEFA Champions League.
"It was a very good response in a very difficult week," said Pellegrini.
"We just lost against Wigan and against Barcelona and we needed to win today. Playing with one player less was very difficult.
"It was a good performance because we defended well with the ball and without the ball, and we also had three good chances to score. It was a very professional response from the players."
Pellegrini preferred to focus on City's performance but did suggest that Kompany had a right to feel aggrieved with his dismissal, saying that referee Lee Mason should have given a foul against Nikica Jelavic before the Belgian hauled down the Hull striker.
"It's clear that before Vincent's foul there is a foul from Jelavic that the referee didn't see and didn't whistle for," said Pellegrini.
"Of course Vincent's foul is a red card but there was a foul from Jelavic before. I don't want to talk about the referee. We won the game and we played very well."
City started the day nine points adrift of leaders Chelsea with three games in hand, and Pellegrini admitted it was crucial to stay in touch.
He said: "We try to respond in the same way we did before.
"Unfortunately it's three weeks since we played in the Premier League so the other teams won their points and we have three games in hand.
"That why it was so important to win the three points today."