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Pellegrini and his players had been heavily criticised in recent weeks for a run of six defeats in their previous eight games that included a 4-2 reverse to United at Old Trafford last weekend and has seen them drop out of contention for the title.
But City produced a much improved performance at the Etihad Stadium on Sunday to see off West Ham with an 18th-minute James Collins own goal and Sergio Aguero's effort in the 36th minute.
"It was very important for our team to win because we had come from two defeats in a row and when one of those defeats is a derby it's worse," Pellegrini said.
"It was very important to try to be a consistent team and I think that we played - especially the first 65 minutes until the injury to David - as a consistent team."
"I think that we played a whole game."
