City trailed 2-1 going into added time before goals from Edin Dzeko and Aguero allowed them to defeat Queens Park Rangers and overhaul Manchester United on goal difference.
"It is a crazy finish to a crazy season," Mancini said. "I have never seen a final like this. This is an incredible moment. We wanted this title and we deserve to win this title. This is for all our supporters, the club, the chairman and the owner."
City ended the season with 89 points and 93 goals and Mancini felt they merited their crown.
"The best team won the title," he said. "The team that scored the most goals, the team that beat United twice and conceded less goals than them."
City scored 18 goals after the 85th minute this season, which Mancini said was a sign of their spirit.
"We showed big character," he said. "I am very proud of my players because they wanted to win this title. To beat a strong team like United is fantastic. We changed the history of this club."
Vincent Kompany, the captain, revealed that many of the team were in tears after Aguero scored.
He said: "It's one big blur for me. I just remember jumping on top of Sergio, he was crying on the floor. All of a sudden it was finished and we won the league.
"I have to be careful what I say but it was one of the best moments of my life together with the birth of my child and my wedding."
Even when City were behind, the Belgian said he thought back to other matches where City scored vital late goals.
"For some reason, it just reminded me of some games like against Tottenham where we won in the last minute, the game against Sunderland where we came back to get a point. This game was crazy. There are no words to explain what happened."
Referring to United's habit of conjuring dramatic late winners, he added: "Miracles do happen in Manchester but on this side of the road this time. It just had to happen for us."
City trailed United by eight points after last month's defeat at Arsenal and, while Mancini publicly insisted the title race was "finished", he later said that was a psychological ploy
"I said this because I wanted to take pressure of us," he said. "After we dominated for 28 games, I was sure we had another chance."
Mario Balotelli said as he was leaving the pitch: "This proves that we are the best. That's why we won. The season's been good, so we deserve to win.
"Personally, too many people talk and say bad things about me. Now, they just have to shut up. Man City is a great club and a great team, and I don't see my future far from here."
Pablo Zabaleta, told BBC Radio 5 live: "When we scored the second goal I thought we were going to win the game. At 2-1 I thought the game was gone. When you fight to the end sometimes you can get it, and I'm really proud to be honest for this group; players, staff and fans. You have to try to the end.
"We won the game in the last five minutes. It's crazy but I think we deserved it. We have fantastic players, and for this club it is a great step forward. Europe's next."
Mark Hughes, the QPR coach and former City manager who signed six of the players Mancini used, said: "It's nothing to do with me. The credit is totally theirs. I don't think have ever been involved in anything like that."
QPR stayed up because Bolton Wanderers could only draw at Stoke City and Hughes said: "It's a huge achievement. This club will never be in that situation again when I am at it."
He did not try to defend his dismissed captain Joey Barton, adding: "He should have been sent off, absolutely."
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