The Portuguese boss jumped into the crowd to celebrate Fernando Torres' stoppage-time winning goal during the Blues 2-1 victory over the Citizens at Stamford Bridge, which angered the City head coach.
"If they feel I did something wrong, I apologise," Mourinho said in his press conference. "This is the drama of the last minute. He [Pellegrini] lost the game in the last minute, and I have sympathy with that.
"In other countries and cultures we shake hands before the game, and that is it. If he was sad because of the result I understand, if he was sad because I did something wrong, I accept that too."
Chelsea moved up to second in the Premier League table with the win.