The City shot-stopper was criticised following his below-par performance during England's narrow victory over Scotland in the mid-week friendly at Wembley.
The 26-year-old was at fault for Scotland's first goal although England manager Roy Hodgson has already thrown his support behind his first-choice keeper.
And City boss Pellegrini said: "I haven't spoken with him but Joe has to demonstrate why he is the best goalkeeper in England every week he plays.
"He is a very important goalkeeper and I have a lot of trust in him.
"Everyone can make an error in one match but personally I have a lot of trust in Joe Hart.
"I don't have any problems with his performance and I am sure he will again demonstrate why he is the number one in England."