Hart had a fine game, making a number of saves in an open encounter, including a penalty stop from Roberto Soldado.
Pellegrini said: "Joe is the number one keeper of England. He made important saves.
"You will all remember the penalty, which was a good save, but he also made a good save early in the first half.
"But when we win the game it's not just because of one of two players. It's about the whole team performance.
"When you score four goals as Kun did or you make so many good saves as Joe did, then of course it's very important to our team, but it's not fair if you don't talk about what James Milner did or (Vincent) Kompany or (Bacary) Sagna."
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