Hart was left out of the side for Saturday's clash with Norwich City following a number of recent mistakes, including the one that presented Fernando Torres with a winning goal for Chelsea last weekend.
Costel Pantilimon came in against the Canaries and had a comfortable afternoon in a crushing 7-0 victory, meaning Hart will have to wait for his next opportunity.
Pellegrini is not sure when Hart will play next but has backed the England international to return to his best form in time.
"Joe needs a rest. I think it will be useful for him," said the Manchester City manager.
"He played the last two years and had every match here. Every player can have a bad moment.
"We will work hard behind Joe so we can return him to his normal performance as soon as possible."
Pellegrini added: "I don't know when he will be back in the team but he knows he must work very hard.
"He has the support of myself and all the players.
"He is the No.1 here in England and I am sure he will return to the normal performances he's had in the last two years."