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City scored two stoppage-time goals to get the win they needed to pip Manchester United on goal difference.
"We have beaten Unitedtwo times, we have scored more than them and conceded less so we deserve it," Mancini said.
"I never gave up. It was a crazy finish to the game and the season but the best team won the title."
Mancini publicly wrote off his side's chances when City trailed United by eight points on 8 April but says that privately he never lost hope.
"When I said the title was over a few weeks ago it was because I wanted to take the pressure off," Mancini explained.
"I was sure we would have another chance. We now need to improve and I am very happy because for an Italian to win the title here in England is fantastic for all Italian people."
While United faltered, Mancini's side won their last six games - including vital wins over their neighbours and Newcastle in the past fortnight - to draw level on points at the top of the table.
That left City knowing a a victory over QPR on Sunday would deliver a first league title since 1968.
City led 1-0 at half-time but QPR hit back with two second-half goals and, even after the visitors had Joey Barton sent off, the home side could find no way through against the 10 men.
Manchester City will hold an open-top bus tour in Manchester on Monday 14 May to celebrate their first Premier League title.
A bus carrying the team will departing from Albert Square at 18:30 BST before taking a 1.8 mile route through the city centre.
With time running out, and United beating Sunderland, Edin Dzeko levelled from a corner before Mario Balotelli set up Sergio Aguero for a 94th-minute winner that decided the outcome of the title race.
"It was just incredible but the result was right and we deserved to win this game," added Mancini, who wrapped himself in an Italian flag at the final whistle.
"I never gave up. I always hoped that Sunderland could score a goal but it was a crazy finish to the game and the season. I have never seen one like this.
"I have never known a moment like this when we scored those two goals and I am so proud of my players because they wanted to win this title so much. They wanted to win this title until the last minute of the season and they proved it here.
"To beat a strong team like United is fantastic. We have changed the history of this club and for that we should be proud. We deserved this and so do all our supporters.
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"It was good that Mario Balotelli was involved in the assist for Sergio's goal and it was right that Sergio should score the goal.
"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. This is the perfect finale for a crazy season."
City's assistant manager David Platt admitted his side made it as difficult as possible for themselves against Rangers but says they want to build on their title success.
Platt told BBC Radio 5 live: "In the space of 20 minutes in the second half we were staring down the abyss.
"But football has astonished me today. It's been absolutely bizarre. I can't put my emotions into words. We now have the experience of winning something, and we'll enjoy it now.
"For Roberto Mancini, he'll enjoy it tonight but tomorrow this will be gone. We go again."
Manchester City boss Roberto Mancini says his side deserved their Premier League crown after snatching the title with a