United saw their local rivals triumph on goal difference last term with a last-gasp goal from Sergio Aguero sealing a first title in 44 years.
But the Red Devils fought back this season and reclaimed the crown with four games to spare, with City boss Roberto Mancini being sacked soon after, and Vidic believes the team spirit within the squad saw them better their neighbours.
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"I think we’ve had 20 players who have scored goals this season which is amazing. It shows how good the spirit is within the team and how hard we pushed to win this title. Obviously, with all the good work on the training ground, we’ve managed that.
"You saw the players at the parade jumping and singing the songs and we had a good time sharing the title with the fans - they deserve it as they support us all year. It’s been a great comeback after last year and we deserved to win this title."
Sir Alex Ferguson bows out at Old Trafford having won a 13th Premier League crown, the last of his 38 trophies over a 26-year tenure, and Vidic has hailed the impact of the Scot during his time at the club.
"It was a real pleasure to play for the manager," Vidic continued. "It's always difficult to talk about him as he was my manager!
"Now I can express myself and have to say he's a great person who always cares about his players and he's always driving them forward. He believes in them and that's why the players always like to play for him. It's a pleasure to play for this club and for this manager."