Vieira has been suspended by the English FA for two Premier League games and an FA Cup replay for kicking out at Stoke City's Glenn Whelan in Tuesday's league match.
"Patrick made a mistake, now we won't have him for three important matches and it will be a problem," Mancini told a news conference.
"I have not spoken to him yet but I will see him. But it is difficult for us. Patrick needs to play at this moment, we have three big games coming up and he won't be playing."
The 33-year-old Frenchman, who had said he would accept the violent conduct charge, will sit out Sunday's Premier League game with fifth-placed Liverpool, one point below City, as well as an FA Cup replay with Stoke and next week's league game at leaders Chelsea.
RED CARDS
Vieira was no stranger to disciplinary action during his time with Arsenal when he was sent off eight times in nine seasons and he said in an interview in the French sports paper L'Equipe on Friday his move to Manchester City could damage his image in England.
"After you've spent so much time playing for such a club as Arsenal, winning titles and playing some of the best football that was played at that time, it is always a bit risky (to come back to the same league in another club)," Vieira said.
"I am not the same player as the one who used to play for Arsenal... I am a different player because I won't be as attack-minded as in my years at Arsenal," added Vieira in the interview, which took place before he was charged by the FA.
"Instead of running box to box 10 times a game, maybe I'll do it five times a game. But I'll have to chose the right moments to do it thanks to my experience. I'll play more with my head."
Vieira returned to the Premier League on loan from Inter Milan last month. Before moving to Italy in 2005, he spent nine years at Arsenal, winning three Premier League titles and four FA Cups.
Vieira was making only his fourth appearance for City against Stoke.
"I still lack pace...There is room for improvement and I think I'm only playing at 60 or 70 percent of my best," Vieira said.
'When PSG went 1-0 up against Liverpool, all of a sudden I started getting abused. At the end of the game, I felt like I grew 10 feet walking around Anfield!': Manchester United legend reveals sitting in home end of Champions League clash
'It’s unacceptable for Arsenal to be making the same mistakes year-after-year with the same manager': Gunners legend makes huge Mikel Arteta claim after Premier League failings
