England international believes he could have saved the winning spot-kick at Stamford Bridge but expects team to bounce back against Arsenal and prove their title credentials
The City and England No.1 admits trying to get into Lampard's head as he was preparing to take the kick and is disappointed to have failed.
Hart told The Sun: "As soon as the penalty was given I was talking to him. I realised the enormous pressure he was under, he'd just come on as sub and this was a massive moment, not just for him, but in the match.
"Right away I was telling him 'I know exactly what you're going to do Frank. I know exactly where you're going to put it'. He didn't react at all but I know he could hear me and he admitted as much afterwards.
"But credit to Frank because he didn't say anything back, he just kept his head down.
"It is so annoying. I should have known what he was going to do.
"Now I can't get it out of my head. It just won't leave me. I can't stop thinking about it. I know I have to move on but this is really bugging me.
"It was so important for us and, knowing Frank like I do, I think I should have known where he was going. We do penalties together every day when we are with England — so I should have known."
Hart also believes that his team-mates could have remained unbeaten for the entire season but insists that losing their undefeated record and an exit from the Champions League does not mean the club is going through a tough time.
He said: "I honestly didn't think it was inevitable we would lose a game. We certainly had no intention of losing a match so it was a big, big blow to be beaten.
"Yeah, it hurts but you have to know how to lose even though you don't want to.
"We will leave other people to speculate about our season and our title credentials. We are thinking just about us and what we need to do.
"We know there will be even more scrutiny now.
"But there is no crisis here, we are not in a barren run. We are still creating chances, still scoring and, hopefully, we will put everything right again on Sunday. We'll dust ourselves down and be ready for what is now a massive game against Arsenal."
The game against the Gunners is another big test for Roberto Mancini's side with the Londoners in fine form, thanks in part to Robin van Persie's goalscoring exploits, which will be sure to test Hart.
"Every single game is a huge test for us because of what we are trying to achieve here," Hart continued. "It's a massive pressure playing for our club.
"But it's only a pressure because we are a good team and we should be winning every game. That's a good pressure and we should embrace it because we are very lucky, we are blessed.
"And we have a great chance in the league. I think we can do it. We are top of the pile and I couldn't care less who is chasing us.
"It doesn't make any difference to me if it's Manchester United or not. We want to keep everyone behind us.
"We are not trying to prove anything to anybody, we're not doing it so we can say 'Shut your mouth, look what we have done!'. We are doing it because we all want to be winners."