The former Arsenal midfielder scored two headers to put City well on their way to a 5-0 FA Cup fourth round replay victory over Notts County at Eastlands on Sunday.
Club captain Carlos Tevez, Edin Dzeko and Micah Richards chipped in with goals in the final six minutes to give the scoreline a slightly unfair reflection on County. But it was Vieira's goals, coming either side of half-time, which ensured City's progress as they had found themselves under pressure from the League One side.
Mancini has used the 34-year-old mainly in cup competitions and the Europa League but that does not mean he does not value the former France international, who doubled his tally of goals for the season.
"He knows the position and it is important that when he plays he plays well," said the City boss. "It is because of that kind of professionalism that I say we want to find another Patrick.
"He has won everything and is a good player, but it's not easy for a player like him to play a lot because of his body. He is 34 now and the time goes for everyone. Time passes for all players. If we find a player like Patrick for our future it would be fantastic as he was one of the best midfielders in the world for a long time."