The England number one produced several outstanding saves before Mario Balotelli struck a late penalty to snatch a 1-1 draw. Dortmund keeper Roman Weidenfeller was also kept busy in an end-to-end encounter, but the visitors had looked on course for victory after Marco Reus pounced on a Jack Rodwell mistake after 62 minutes.
Mancini said: "Joe Hart saved us from an incredible defeat because he saved everything and we should say thank you to him."
Hart's performance drew high praise from his England team-mate - and Manchester United striker - Wayne Rooney during the match. Rooney tweeted: "Have to say joe hart has been incredible. For me best keeper in the world."
When was asked whether it was the best goalkeeping display he had ever seen, Mancini 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."
The half-time score could easily have been 3-3, rather than 0-0, as both teams looked to attack, but Mancini was disappointed by his side's efforts. The result leaves them with just one point from their opening two fixtures in the competition and facing an uphill fight with back-to-back fixtures against Ajax to come next.
City have also still not kept a clean sheet all season and, despite Hart's brilliance, their defence is a concern.
Mancini said: "We didn't play well. We conceded a lot of chances to them and I am really disappointed by our performance. The Champions League is totally different from the championship. When you have a chance you need to score. If you concede like we concede this evening, it is hard to win."
City equalised in the last minute through substitute Balotelli after Neven Subotic was harshly judged to have handled at point-blank range as Aguero hooked the ball toward goal.
Mancini said: "It was important - Mario's penalties are like Joe in goal. He did very well. I am happy because he scored. Our performance was very, very poor, but at the end of the group this point could be very important."
Source: PA
Source: PA