During Tevez's absence, City have booked their Wembley place with a 1-0 win over Manchester United and followed up with Barclays Premier League victories away at Blackburn and at home to West Ham.
"When Carlos is out we are missing a fantastic striker," said Mancini. "He is an important player for us and has scored more than 20 goals this year.
"But if we want to improve as a team and keep on winning we have to be able to perform without key players, whether it be Carlos, Yaya Toure or David Silva. We have shown we can do that. We have built a team this year.
"We have bought a lot of good players, and the great thing is when one or two have been missing we have still had a team. We always have a team, and this way, we can improve everything.