Nastasic inadvertently headed the ball beyond an outrushing Hart, leaving Torres the simplest of tasks to seal a last-minute victory which moved Chelsea up to second in the Premier League and left City in seventh, six points behind leaders Arsenal.
Hart has faced mounting criticism for a number of mistakes this year at club and international level, with England manager Roy Hodgson and City boss Manuel Pellegrini both publicly backing the 26-year-old in the past month.
Chilean Pellegrini, in his first season in charge at City, was slightly less forthcoming in the aftermath of Sunday's defeat, however, the side's third in the league after also losing at Cardiff City and Aston Villa.
"What I think, I won't talk about," Pellegrini said after the match.
"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," he added.
"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."
After the goal, Hart was captured on camera yelling "keepers", indicating that he had called to take control of the ball, but that did not stop many suggesting it was his error that led to the winner.
"Wow. Torres deserved a goal today. Hart at fault though," former England and Liverpool striker Michael Owen said on Twitter. "He only needs to stand on his 6 yard box and Nastasic nods it back to him."
That view was echoed by former Liverpool manager Graeme Souness on Sky's Super Sunday.
"It was 100 percent Joe Hart's fault. A large part of goalkeeping is making the right decision - when to come for a cross, when to leave your box and Joe's just got it wrong there; he came, he shuffled to go backwards and then came again.
"Nastasic is watching the ball come out of the sky, it's over his shoulder and he's in complete command.
"It's hard to put on Joe because he's having a difficult season but I'm sorry, we're here to call and it's his fault today."
Hart was deemed at fault for two of Bayern Munich's goals in his side's 3-1 Champions League defeat at the start of October, less than a week after failing to close down Aston Villa's Andreas Weimann in a 3-2 loss in the Premier League.