Tevez scored both goals as the Blues came from behind to claim a precious 2-1 first-leg victory at Eastlands to set up the decider next Wednesday.
"I am very happy for Carlos," said Mancini.
"He is an ex-Manchester United player so this game was very important for him. To score two goals was excellent."
Mancini added: "It is not a big advantage, but it is an advantage.
"I am happy with the result because we were behind after 20 minutes and I felt it could be difficult.
"But we recovered, scored two goals and played well.
"They had three or four chances but, in Shay Given, we have one of the best goalkeepers.
"Now I would say we have a 51% chance."