Tevez has not played since he tore his hamstring in City's 3-0 defeat at Liverpool in April and, while he is making good progress, he remains on the sidelines and is unlikley to play against Everton this weekend.
Mancini says if the Argentinian cannot prove his fitness before next Tuesday's clash with Spurs then he will be ruled out of the Cup final against Stoke a week on Saturday.
"It's very difficult for him to play against Everton," said Mancini.
"If he doesn't play against Tottenham, it will be impossible for Carlos to play in the final."
Micah Richards, however, is likely to be fit for the Stoke showdown as he has now virtually fully recovered from his hamstring problem.
"Micah is very close," added the City boss.