Although City struggled before the break, Edin Dzeko and David Silva both wasted good chances late on as the visitors came to dominate the game and Mancini was clearly annoyed.
"I thought the first half was so-so because Swansea played very well," the Italian told Sky Sports.
"In the second half we missed some incredible chances. We had five chances to score - two in the first half and three in the second.
"In the second half we dominated this game so I am happy with the performance but unhappy with the goal we are missing."
Part of the problem in the first half was a lacklustre display from Yaya Toure, who was withdrawn at the interval, and Mancini admitted that the Ivory Coast international was not fully fit.
"Yaya had a problem in the warm-up and he was not 100 per cent," he added.
"We had a big problem in the middle to stop their counter attack. We took him off because we didn't want to take a risk for the next game."
Thoughts will soon turn to the FA Cup final against Wigan next weekend but Mancini is keen to focus first on a Premier League clash at home to West Brom in midweek.
"Before the FA Cup final we have another important game on Tuesday because we need to get the second position," he said.
"After that we will prepare for the next game against Wigan."