The City boss believes his players were fatigued after the defeat in Amsterdam in midweek and took a while to get going against the South Wales outfit.
“It was important we won this game because we have just played a difficult Champions League match and now we have a few days’ rest because we have no midweek game,” said Mancini.
“We were tired and I think it showed in the first half, but we played better in the second-half so I am happy.
“Swansea were fresher and played very well so I am very pleased we won this game, even if we weren’t at our best. They showed what a good side they were last year and they are doing the same again this season.”
Mancini also had praise for match-winner Carlos Tevez – who turned in a hard-working display for the record 102 minutes played against the Swans as well as giving a brief update on the Micah Richards injury.
“Carlos played very well against West Brom and again today – he worked very hard and I am very pleased for him,” he said.
“He scored a good goal at an important time and is a vital player for this team,” he said. “I’m not sure what Micah has done yet – we think he has a problem with his knee but we won’t know until next week, but I obviously hope he will be OK.”
Gareth Barry also says the result was more important than the display on this occasion, adding: “It was a massive three points. Three games in seven days is always tough.
“It wasn’t a great performance, but the manager said at half-time to stay calm and we’d get a goal. Carlos came up with the goods but to be fair to them, their game plan was good. They sat deep and made it hard for us to get the ball to our forwards so we’re happy with the win.”
Swansea boss Michael Laudrup was pleased with his side’s performance, but thought his players should be travelling home with a point at least.
“If we look at the game, we knew the first 15 minutes would be difficult and that City would come out and try to come at us,” he said.
“City didn’t create too many chances and we were in the match throughout – but then Carlos Tevez scores a goal out of nothing. We had two great chances of our own with Michu but Joe Hart saved well on both occasions.
“When you come away to the champions and restrict them to just one chance, you can’t be too down-hearted. Great teams take their chances and City did – we missed ours and that was the difference today.”