A lack of cutting edge in front of goal has been a familiar bugbear of Mancini's this term as City have surrendered the Barclays Premier League title to rivals United.
Such failings were on display once more at the Liberty Stadium, with substitute Edin Dzeko the main culprit as he passed up a gilt-edged opportunity in the closing stages.
Mancini also felt Dzeko should have been awarded a penalty after the Bosnia international striker went over Chico Flores' trailing leg, although he claimed not to have seen a first-half incident when Swans top scorer Michu had strong claims rejected after Matija Nastasic sent him tumbling.
"We deserved to win as we missed a lot of chances," he said. "We had three incredible chances in the first half and two or three in the second half, and a penalty that I don't know why the referee did not give.
"I am not 100 per cent sure it was a penalty, I am 200 per cent sure. It was impossible not to get a penalty for that.
"I did not see Swansea's appeal, I saw ours as it was close to the bench, it was incredible."
On Dzeko's miss-of-the-season contender, Mancini added: "I think we are very sorry as he played well and deserved to score."
Mancini also alleviated any fears Yaya Toure may have picked up an injury just a week before the FA Cup final.
The Ivory Coast international was taken off at the interval but Mancini said: "He was tired and we thought it was better to bring him off."