Mancini was pleased with Tevez's cameo and paid tribute to his side's determination to win the game.
"I'm happy, because he did well," Mancini told Sky Sports 1. "Also he's not in good form, I don't think he's fit 100%, but that's football.
"I think we deserved to win because we had three or four chances in the first 20 minutes.
"When they (Chelsea) scored I think we didn't deserve to go behind. But we wanted, we desired to win this game."
He admitted, though, he was feeling nervous when Chelsea took the lead.
"After their goal it was feeling like squeaky bum time," he added.
Mancini claimed City's title bid was now back on track following their defeat at Swansea.
"Yes, I think so," he said. "It's more than three points this game."