Hart failed to save Darren Fletcher’s stunning shot and says he is annoyed by every goal he lets in, despite the emphatic nature of the result in the derby clash.
He told the club's official website: "I was annoyed. You can get carried away with the result and the three points, but we let in a goal. It kills me to let one in, it kills all of us.
"I'm so angry because we've hammered teams and then we've let a stupid goal in. It's frustrating, and we're trying for perfection at the moment.
"I try and be there when I'm required. I have bits to do, other than that, I stay out of the way.
"We're doing our jobs at the back, which is all we need to do with the attack we've got. We're happy to just go about our business unnoticed and let the lads up front score the goals."
City face Wolves on the Saturday and Hart is not expecting an easy encounter.
He said: "Wolves are going to be tough, they're struggling and need the points as much as we do. I grew up with Dave Edwards. He scored the winner against me last time at their place, but I hope he plays."