Mancini will be looking to get City's Champions League campaign back on track at the Etihad Stadium.
City will face a stern test of their Premier League title credentials at Old Trafford on Sunday, having climbed above their local rivals at the top of the table over the weekend.
Mancini does not think such a game requires extensive preparation and instead wants to make sure his players stay focused on the European clash with Villarreal on Tuesday.
Having taken just one point from their opening two games in Group A, the City boss recognises that it is crucial to pick up a victory to boost their hopes of reaching the last 16.
"It is important for us to concentrate on Villarreal." Mancini said in the Daily Telegraph.
"If we can beat Villarreal - and I don't think it will be easy - maybe we will have a better chance to go through to the knockout stages. If we don't beat them, it will be difficult."
Asked if it was a bigger game than the clash against United, Mancini added: "Yes.
"After Villarreal, we have four days to recover and to prepare for the derby. We don't really need to prepare for the game with United because we know they are a top team, and I don't think we need to prepare any differently.
"Beating Villarreal is our first target. Then we can think about the other games.
"We are playing in the Champions League for the first time and we can't think that we will win every game.
"We know we need more experience, but we still have four games left and, if we beat Villarreal, we can still get first place in the group. If not, we can fight for the second place."