The England number one produced several outstanding saves before Mario Balotelli struck a contentious late penalty to snatch a 1-1 draw in a pulsating Group D clash at the Etihad Stadium.
Mancini said: "Joe Hart saved us from an incredible defeat because he saved everything and we should say thank you to him."
Mancini was asked whether it was the best goalkeeping display he had ever seen.
The Italian said: "I don't know this. He did a fantastic performance, he was fantastic tonight. I don't know if it is the best performance in football history, but he did very well."