Roberto Mancini's side trail league leaders Manchester United by 12 points with just seven games remaining, and the Frenchman feels that they should have maintained a stronger challenge against their local rivals.
"The only thing you don't want in football is regret, if you lose against a better side then that's it, hands up, you have to accept it," Clichy told the Daily Mail.
"But when you feel deep inside that they are not better than you, you will always regret it and then that's hard. It makes you angry and disappointed. We should do better.
"I don't believe [United] have been better than us. But we have had games where we have been the best team but have not won. We have thrown so many games away."
City play Chelsea in the FA Cup semi-final at Wembley on Sunday.