Manuel Pellegrini refused to offer Joe Hart a public show of support after the England goalkeeper's last-minute rush of blood presented Fernando Torres with Chelsea's winner and left Manchester City six points from the top of the Premier League.

Matija Nastasic's nodded back-pass looped over the onrushing Hart, who ended up well outside his penalty area, with Torres capping a fine performance by running through to convert only his second league goal of 2013. Hart's reaction, shouting "keeper's, fucking keeper's" as he retrieved the ball from his net, suggested he had attempted to warn Nastasic.

But his decision to tear out of the box did appear rash and similar to his error against Aston Villa last month which presented Andreas Weimann with a winner. There have been other high-profile errors, against Bayern Munich's Franck Ribéry and Arjen Robben, and Cardiff's Fraizer Campbell, as well as against Scotland with England. Indeed, Torres's winner was remarkably similar to Nikola Kalinic's goal for Blackburn at City three years ago, suggesting lessons have not been learned.

"What I think, I won't talk about," said Pellegrini, who was left infuriated by his opposite number José Mourinho's celebrations after Chelsea's winner. "I repeat that the analysis I do with individual players I do with the players, not the press. You must ask [Hart] how his confidence is.

"I talk just internally with the players. We are going to see the best way to arrange things. We are losing stupid points. The three defeats we had away we didn't deserve but the reality is we have lost them and we've had the important responsibility for the goals the other team scored. We try to arrange. We have time."

The Chilean confirmed he had declined to shake Mourinho's hand after the final whistle having been exasperated that the Chelsea manager ran across the visitors' technical area to celebrate with the supporters behind the dug-out. "I don't speak about him," he said. "I didn't expect anything else. It is a different way to celebrate from me. No, I didn't shake hands because I didn't want to."

Mourinho claimed he had jumped into that section of the support because his son, José Jr, was sitting there. "Chelsea is guilty because I want to buy a season ticket for my son and they give them a season ticket behind the away dug-out," he said. "I went for him, I promise. But this is the drama: I beat City in the last minute in Madrid and I slid on my trousers and ripped them; I conceded an equaliser in the last minute against Bayern Munich and [it felt as if] somebody put a knife in my back. This is the emotion. If they believe my son is there, great. If they don't believe, I apologise if they feel I did something wrong."

The victory, spurred by Torres's effervescent display and Ramires's tireless running in midfield, appeared significant for the hosts as they inflicted psychological damage upon direct rivals for the title. City have enjoyed the upper hand over Chelsea in the past year.

"But I watched all those games – at Wembley [FA Cup semi-final], the game at home, the game away, parts even of the friendlies in the United States – [the issue] was mental, not tactical," said Mourinho, who confirmed he would play a weakened team in Tuesday's Capital One Cup fourth-round tie at Arsenal.

"Some people tell me that I have now gone 65 matches at home unbeaten [in the Premier League] but that's not right. I have gone five matches. The past is the past.