Manchester City endured a miserable night at Liverpool on Monday as they went down to a 3-0 defeat, conceding three goals in the first half.
To make matters worse, Tevez was forced out of the game after just 16 minutes and confirmed to a touchline reporter that he believed the injury was "bad".
The news comes just days before City's FA Cup semi-final against arch rivals Manchester United and Mancini confirmed his captain is almost certain to miss the game. "I think that it is very difficult for Saturday," he told Sky Sports.
Mancini then confirmed the player's hamstring is torn but, asked if it would rule him out for the season, he said: "No, no, no. I don't think so.
"We'll try [to get him fit for the FA Cup semi-final] but we probably need two weeks. I don't think he will play. We will try to recover him but it is very difficult because we also have to think about the other six games for Champions League [qualification]."
Mancini also said he was to blame for the defeat at Anfield as he "made a mistake" but he refused to elaborate.
"Tonight I made a mistake," he said. "It was my fault. I think the players can do better, but I made a mistake. I know [what the mistake was]. It is for me. I am sorry for the fans. We only started to play after 20 minutes."
In his press conference after the game, he added: "I made a mistake in the last two days. I know why. It is important I understand this for the next game. It was my mistake because we did not prepare very well.
"I made three changes, bringing in three fresh players. Our focus was not good. Liverpool played fantastically in the first 20 minutes, we left a lot of space for them, and they were very aggressive at the start and we played very soft.
"After 20 minutes we started to play but it was late. For this, it is my fault. It is important for me to understand this."