Tevez scored the stylish opening goal of the 2-0 victory then set up midfielder Yaya Toure for the Blues' second to confirm City's second away win in three days after the Salzburg celebrations.
Mancini told City's website: "I am very happy for Carlos. It was an important goal for him to score. He probably hasn't been in 100 per cent form - he didn't work for one month after the World Cup - but this goal will help.
"But if we want to win something, we must also understand we have to learn to play without Carlos and without Yaya, and be a team who can win without these players, because we play every few days and this is very difficult."