City boss Mancini took the blame for his side's 3-0 Premier League defeat by Liverpool at Anfield, although he was not willing to divulge why.
There was surprise before kick-off when it emerged that Mancini had left Nigel de Jong and David Silva on the bench.
"Tonight I made a mistake, it was my fault," he said. "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."
Mancini's night was soured further with star striker Tevez forced off after just 16 minutes with a hamstring injury.
The Italian admitted Tevez would struggle to be fit for Saturday's FA Cup semi-final against Manchester United at Wembley.
"His hamstring is very difficult for Saturday," said Mancini. "It is very difficult as it is only five days away.
"We'll try (to get him fit) but we probably need two weeks."