The City manager attempted to lure the Netherlands international from Arsenal to the Premier League champions in the summer, but the forward opted to join the Red Devils.
Van Persie has since scored 20 goals in 26 appearances for Sir Alex Ferguson’s side, including a late winner in a 3-2 victory at the Etihad, prompting Mancini to declare the former Gunners captain is the difference between City and United this season.
“Those words were a motivation for the strikers,” said Tévez.
“I’ll try to help us to compete in the League and Cup, and try to win both.”
City are 17 points behind Ferguson’s side in the Premier League table, while Mancini’s men also suffered a premature exit from the Champions League at the group stage.
However, the Argentina international has vowed to help City overturn United’s lead and retain their top-flight title, while the Citizens striker also has his eye on a FA Cup winners’ medal.
“There’s a long way to go and a lot of games to play,” he added.
“The emotion of the Premier League means it’s always a fight to the end. If United lose one game, we’ll be getting close to them. They will know that.”
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