The Blues looked set to endure a awful afternoon when Djibril Cisse and Jamie Mackie overturned Pablo Zabaleta's first-half strike in between Joey Barton getting sent off.
But Edin Dzeko rose to give the Blues fresh hope before Sergio Aguero drove home the goal that turned City into champions for the first time since 1968.
Mancini told Sky Sports 1: "It was incredible - they deserved this. To win it like this is incredible. I don't think I've ever seen a finale like this.
"We didn't deserve to lose, we had a lot of chances and we deserved to win the game and championship.
"It's fantastic for the club and the supporters after 44 years. It's been a crazy season and a crazy last minute.
"Five minutes from the end, I didn't think we'd win this game. But we deserved to win this and deserved to win the title. We were on top for 20 games.
"I think for us it was really important to start winning this championship, Manchester City can have a big future now."
City captain Vincent Kompany admitted the dramatic ending was almost too much for him.
"You want to say it's the best moment of your life but, if I'm honest, please never again this way.
"Even though the first half was really good we just couldn't get through.
"I never stopped believing. When Edin scored that goal, it reminded me of so many other moments during the season when we've done this before. There was no reason not to believe.
"It's not sunk in yet. I don't know what happened at the end, it was just a huge mess.
"I'm so happy for the guys cos they've given so much this season. We've dreamed of this all our lives and now we're champions. See the fans and how happy they are - unbelievable."
Mike Summerbee, a key member of the last City side to win the league in 1968, seemed in a state of shock.
"It was quite unbelievable, you couldn't write that," he said.
"I thought we were out of it, then things change. I can't go through things like that at my age."
Former team mate Francis Lee said it was high time a new generation took over.
"I think we've got a new band of legends now," he said. "We can retire into the legends club and just sit there with our feet up now."
United manager Alex Ferguson was taken aback by the most extraordinary close to a Premier League season but still found time for a dig at the side he previously dismissed "noisy neighbours".
"Nobody expected that. Everybody expected City to win, but they did it against 10 men for half an hour and with five extra minutes to help them," he said after Wayne Rooney's goal had put him in sight of the title.
"But I congratulate City on winning the league. Anybody who wins it deserves it, because it's a long haul. At the end of our game our players didn't actually know the results. Now, they're really disappointed, I'm glad to say.
"There's no other way they should be. They conducted themselves brilliantly today. Their performance level was good. I'm pleased at our performance this season. 89 points would win most leagues. It wasn't our turn today."