Just a day after receiving backing from England manager Roy Hodgson, Pellegrini too got behind the 26-year-old stopper.
“Of course he feels that he didn’t do very well [against Bayern Munich], but I think he doesn’t have any problem. He is continuing with the team and with our trust we hope he will recover from the game,” said the Chilean.
“After the game I always speak with all the players. I spoke with Joe and we analysed what we did in the game.
“Joe knows he must improve the way he is playing, but he knows he has our trust.”
City come up against Everton in the Premier League tomorrow, the only team who remain unbeaten so far this campaign.
Pellegrini admitted he has not yet decided on his starting eleven and is giving it a lot of consideration.
“I will decide tomorrow who will start, I don’t tell you now that Joe hart will play tomorrow, because the players don’t know yet,” he said.
“I think he [Hart] is being pushed hard enough. Costel Pantilimon is a good keeper also; he has all the right attributes to play. He’s working hard and I’m sure that if he must play tomorrow or another day, he will do well.”
The manager also revealed that Jack Rodwell is back training with the first team and that apart from the long-term injured Martin Demichelis and Stevan Jovetic, he has a full squad to choose from for tomorrow’s game.
“Jack just started working with the whole squad yesterday. He is fit, but he will not be included tomorrow, but he is fit,” he said.
“Everybody else is fit, apart from Jovetic who has a couple of small problems.”
The full press conference will be on CityTV this afternoon.