Manchester City boss Manuel Pellegrini refused to publicly back Joe Hart after another error from the England goalkeeper saw Chelsea triumph at Stamford Bridge.
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.
"I do it privately with the players," Pellegrini said.
After defeats at Cardiff and Aston Villa, the Chilean was left to rue the further loss of "stupid points" away from home.
"We repeat the story," he said.
"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."
Pellegrini was incensed and at the final whistle refused to shake hands with Chelsea boss Jose Mourinho, who celebrated the goal with supporters behind the visitors' dugout.
Pellegrini said: "I didn't shake hands. I didn't want to shake hands."
Mourinho had no complaints with Pellegrini and insisted he entered the crowd to share his joy with his son, who has a season ticket.
"I don't feel it is a lack of respect," Mourinho said.
"If he was sad because of the result, I understand. If he was sad thinking that I was doing something wrong by going to celebrate there, I accept that too. No problem."
He added: "Chelsea is guilty. They have to give my kid tickets behind my dugout."
Mourinho was thrilled with Torres' response to his early miss.
The £50million frontman missed a sitter, set up Andre Schurrle's opener, hit the crossbar and then netted the decisive goal - his first Barclays Premier League goal of the season and second of 2013 - after Sergio Aguero's stunning equaliser.
"When a striker misses an easy early chance, many times he's affected for the rest of the game," Mourinho said.
"It looks like that moment was the moment where Fernando thought 'I will be the man of the match'.
"The goal comes in a very intelligent action by Fernando. (A) misunderstanding by Joe and Nastasic, but Fernando was very clever.
"He's sharp, he's powerful, the belief is high. We are happy for him, but we are all happy because it's a very important victory against a team we couldn't beat last year."