Tevez scored the second goal in City's 3-2 triumph over Chelsea at Villa Park with Yaya Toure and Samir Nasri also on target for the Barclays Premier League champions.
The Argentine looked hungry and sharp - in contrast to his six-month exile last season before returning to play a key role in the run-in to the title.
Mancini said: "I am very happy because this year Carlos has worked very well in pre-season and his form is better than last year. Also this year he wants to play football. For a player, it is difficult when he does not play. Last season he did not play for six months and this is difficult.
"I expect him to be a very important player. He is a top player if he wants to play. Last year we had Carlos for the last 10 games and it was important because he scored five or six goals.
"But he was not 100 per cent. This year is the first time in four, maybe five years he has done a full pre-season and for every player this is important."