The England goalkeeper was blamed for James Morrison's goal for Scotland this week.
"I haven't spoken with him, maybe tomorrow, but I think Joe Hart has to demonstrate why he is the best goalkeeper in England every week he plays," said Pellegrini.
"He is a very important goalkeeper, I have a lot of trust in him. Everyone can make an error but I have a lot of trust in him and I am sure he will again this year show why is the No 1 in England."
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