City made eight changes to their starting XI in midweek, with one eye firmly locked on Saturday's FA Cup final date with Wigan Athletic.
A slow start suggested Mancini had shuffled his pack too vigorously, but the Blues settled into the game and could have had more than a solitary strike from Edin Dzeko to show for their efforts at the interval.
In the end, one goal was enough to see City to three points and cement their second-place standing in the Premier League table.
Mancini told Sky Sports: "I thought that it was a difficult game. We changed a lot of players, we took some risks, but in the end it was important to win this game.
"After 10 minutes, we started to play very well. We had five incredible chances to score, but we were missing. For that reason, we suffered more in the second half.
"They are a good team. They have had a fantastic season, they play good football. We knew that it would be a difficult game."
Asked if he has now settled on a side for a trip to Wembley this weekend, Mancini added: "Maybe. We have four days. It is important after this game to recover our strength.
"We didn't take a risk with some players. I think so."