Mancini hugged Given at the end of the game after seeing the Irishman make a string of super saves.
"Shay Given made some great saves today and I rate him so highly," he told City's website.
"Shay gives everyone around him a sense of confidence and he can be pleased with his afternoon.
"We have worked hard these last few days and this was the reward for the team and the supporters.
"There were people playing in positions that are perhaps not their normal ones but everyone did well including Robinho who has not had a lot of football after his injury.
"I thought we were better in the first half than the second when we got a little tired. But now we must prepare properly for Wolves."