Hart conceded the spot kick by fouling Demba Ba, handing Lampard the chance to score his 200th Chelsea goal.
Lampard had his strike palmed clear by Hart and City responded to claim a 2-0 win over the side just one place below them in the Premier League table.
The England keeper admitted that stopping his international colleague from netting made the save more special.
He told Sky Sports News: "I work a lot with Lamps on England duty and he is a great penalty taker, he's a big hero of mine if I'm honest.
"It was nice to save it but I'd given it away so I had to save it. We spoke about it but I'm sure it's not mind games with Frank, he's a strong man and knows what he's going to do, so he's not going to be put off by an idiot like me!
"It was a case of trying to go the right way and getting a strong hand on it. I just want to make saves for Manchester City. I enjoyed doing it in this game, its as simple as that."