Injury-time goals from Edin Dzeko and Sergio Aguero secured a 3-2 win for the Blues over QPR, which was enough to give them their first championship since 1968.
"We are happy because we won this trophy after 44 years," he said. "We changed the history of this club by beating a strong team like United. Now I hope we can continue to win."
For most of an agonising second-half, the day looked like becoming the ultimate disaster after first Djibril Cisse, then Jamie Mackie scored for the visitors after Pablo Zabaleta's first-half strike.
It seemed not even the ridiculous dismissal of former Blues midfielder Joey Barton could chance the course of a title race that seemed, once again, certain to end with Manchester United lifting the trophy.
But Mancini had no doubts City deserved their success, having established superiority over United in every department apart from, until the final two minutes, their league position.
"We deserved it," he said.
"We played the best football. We scored the most goals, we conceded the fewest. We beat United twice.
"I have never seen a final like this though. In the history of the club, a final like this does not exist.
"I am very proud of my players though. They wanted to win this title until the last second of the last game."