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."
The Italian added: "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."
Watch: Mancini - Crazy end to crazy season... More Videos
Samir Nasri, a summer signing from Arsenal, was thrilled to taste league success in his first season at the Etihad.
"It's the first time in my life I've won something like this - to be losing 2-1, to come back and score the winning goal to give us the title," he said.
"It's amazing and I'm really happy. I knew I made the right decision (coming here) and tonight [Saturday] I want to celebrate with all our fans, my family and my friends."
Goalscorer Pablo Zabaleta added: "I thought when we were losing 2-1, I thought 'we'll score one goal and we're still going to lose'.
"I don't want to wake up from this. You just look at the players and the fans, everybody deserves this.
"The most important thing for any team is when you believe. If you believe in yourself you win. We believed until the last minute."
Goalkeeper Joe Hart hopes it is the first league title of many for City.
"I'm proud to play for Man City and I'm proud to play with these boys," he said.
"It means the world to these fans - we need to do it again now, let's do it again."
Watch: City players celebrate hard-earned title... More Videos