Gareth Barry finished off bottom club Reading with a controversial headed winner in the 93rd minute at Eastlands on Saturday to move City within three points of United ahead of their rivals' trip to Swansea on Sunday.
It was the fourth time this season City have won a league game with a goal in the 87th minute or later following similar successes against West Bromwich Albion, Fulham and Tottenham and Mancini joked that the stress of his team's performances may yet take their toll.
“I'm very happy but we've had a lot of games like today,” Mancini said. “My heart is not strong enough to take it!
“That win could probably be the difference come the end of the season. I hope so.
“Our attitude is good. We kept our concentration until the very end. We wanted to win this game and we kept going until the very last second.
“This game is important but when you play well, like we did in the first half, if you have a chance to score, you must score. This can change a difficult game.”
City enjoyed all the possession against Brian McDermott's Reading without creating too many clear-cut chances and, while this may not have been a vintage performance by his team, Mancini is happy with the attitude and character being displayed by his side as they end a year in which they were crowned champions.
“We have improved a lot and we want to try until the very end,” added Mancini. “Our attitude is strong. Sometimes you can win these games, sometimes you cannot.
“I think we deserved to win this but when you are in the last two or three minutes of extra time, it can be difficult.
“If you don't score in the first half, when we had a lot of chances to score, then you make it difficult.
“They played very well and defended for 90 minutes with men behind the ball but in the end we only needed one chance and I'm happy for the victory because without it, it was a problem.”
Mancini also feels that there will be more games such as this for the champions in the second half of the season after his players failed to heed his warning that Reading would prove difficult opposition.
“I told the guys before the game that Reading might have conceded a lot of goals the last few games but they are playing well,” said Mancini.
“I told them it would be a difficult game and I think they will find more games like this between now and the end of the season.”
McDermott was left to bemoan his luck once more after seeing Barry climb over defender Nicky Shorey to head in the winner.
Mancini and City claimed there was nothing wrong with Barry's effort, although Reading strongly disagreed.
McDermott and the Royals also thought they should have had a 75th minute penalty when Matija Nastastic might have handled in a move which also saw Jay Tabb apparently fouled by City debutant Karim Rekik.
“It was an absolute joke. We've had that a few times this season,” said McDermott.
“I said to the referee at the end, he'll be gutted he missed that. The ref said he hung in the air but you can hang in the air all day if you're hanging on somebody's back! It was an absolute certainty.
“And he knocked Tabb out of the way, we should have had a penalty. We've had a few of those recently but I just have to look at the positives.”