City replaced United at the top of the Premier League table after defeating Aston Villa 4-1 on Saturday to set up a mouth-watering showdown with Sir Alex Ferguson's reigning champions at Old Trafford next Sunday.
But Mancini's expensively-assembled side are fighting to stay alive in the Champions League after taking one point from their opening two group games.
Failure to defeat Villarreal in Manchester on Tuesday would leave City with a mountain to climb to qualify for the knockout stages from Group A.
And having battled so hard to win a place at European football's top table, Mancini is deperate that City's debut campaign in the Champions League does not end in anti-climax.
"Is Villarreal bigger than United? Yeah. But after Villarreal, we have four days to recover and to prepare for the derby," said Mancini.
"And 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.
"Now it is important for us to concentrate on Villareal. If we can beat Villareall -- 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."
City have found the going tough against Europe's elite so far.
It required a rare goal from Aleksandar Kolarov to rescue a point against Napoli on their Champions League debut at the Etihad Stadium.
And their European campaign erupted in controversy when Carlos Tevez allegedly refused to come off the substitutes bench during a 2-0 defeat against Bayern Munich in Germany last month.
"We know we can lose sometimes and also that we can go out of the Champions League," added former Inter Milan coach Mancini.
"But we have four group games left. And I remember at Lazio, we won the first two games and then after that we picked up only one point from four games -- and we went out.
"I had a difficult time in the Champions League at Inter as well.
"But at least with Inter we always reached the second stage and after that it is always difficult. But for us now, the target is that we want to reach the knockout stages in February."
Sergio Aguero is set to feature but Mancini has yet to decide whether to start with him.
The Argentina international missed the weekend win over Villa with a groin injury but Aguero, who has scored 11 times for club and country this season, is expected to face Villarreal.
"He is getting better. We will decide if he is fit enough to play or be on the bench," said Mancini.
Villarreal have lost both their opening two group games without managing to find the net againt Bayern Munich and Napoli.
And although the Spanish side extended their unbeaten run in La Liga to four games with a goalless draw away to Getafe on Saturday, they have managed to win just one of their opening seven league matches.
So uninspiring is their form that Villarreal president Fernando Roig felt it necessary to speak out in support of under-fire coach Juan Carlos Garrido.
Having overseen the departure of star playmaker Santi Cazorla to big-spending Malaga in the summer, Roig said he is prepared to give Garrido time to get things right.
Source: AFP
Source: AFP