Sterling pulled up early in the first half and was replaced by Fernando while Hart injured himself clearing a short Martin Demichelis back pass.
City boss Pellegrini confirmed that both players had suffered muscular strains and would be out for up to four weeks.
"I don’t think muscle injuries can heal in one week. They normally need three or four weeks," said the Chilean in his post-match press conference.
Joe Hart and Gaël Clichy - Manchester City
Image credit: AFP
Hart has a strained calf while Sterling has a groin injury, and both will miss England's upcoming matches against Germany and the Netherlands next week.
England coach Roy Hodgson is already without Wayne Rooney, Jack Wilshere and Luke Shaw.
However, more worryingly for City, the pair could miss the key Champions League quarter-final tie against PSG.