The City stopper and Matija Nastasic were involved in a mix-up which gifted Fernando Torres a 90th-minute winner.
Following the loss, Pellegrini refused to discuss the errors which resulted in Torres' winner or whether Hart's place is under threat from Costel Pantilimon.
Manuel Pellegrini: "I do it privately with the players.
"After defeats at Cardiff and Aston Villa, we repeat the story.
"We had absolutely the control of the game.
"We played very, very well in the second half.
"We didn't have any problem with Chelsea but finally in the last minute we lost.
"We are losing stupid points."
Source: Manchester City MAD