The goalkeeper gave away the spot-kick in the second half of Sunday's 2-0 victory but then prevented his England team-mate from scoring from 12 yards.
Hart's save was the platform for Yaya Toure and Carlos Tevez to go on and win the game and he was pleased to contribute positively after recent criticism.
Hart, who had come under scrutiny after a poor performance in the loss to Southampton, said: "Lamps is a big hero of mine and it was nice to save it but I gave it away so I had to.
"It was just a case of trying to go the right way and getting a strong hand to it."
The win allowed City to close the gap to Manchester United at the top of the Premier League to 12 points and Toure, who opened the scoring for City, was happy with the result.
He said: "The first half was quite good. We missed a couple of chances and Joe had to make a big save. I think it made the difference.
"Of course we know United are very strong away and at home and it's going to be very tough but we have to keep going."