The Chilean is backing the England international to come good but will not wait indefinitely for him to regain top form.
Pellegrini's words come soon after a similar warning from England boss Roy Hodgson over his spot in the national side.
Hart has made several costly errors for club and country over the past year and had another uncomfortable game as City were surprisingly beaten at promoted Cardiff in the Barclays Premier League last week.
Pellegrini said: "For the moment Joe will continue being our goalkeeper but I spoke with him and he knows he must be quickly in his top form again.
"I am sure he is a top goalkeeper and will do it again.
"I said from the beginning my teams never play with names, they play with performances.
"Joe knows perfectly he needs good performances in the next games. At the moment he has all the trust."
Hart's critics have suggested that a lack of serious competition for his place in the side has been a contributory factor in his loss of form.
At City, back-up Costel Pantilimon has only been used in cup ties over the past two years but Pellegrini insists the Romanian is a serious challenger to Hart.