The City manager was quoted last month as saying Manchester United striker Van Persie could prove the difference between the two teams in the race for the Barclays Premier League title.
Van Persie has been a revelation for the Old Trafford club since his summer switch from Arsenal, and has already scored 16 league goals this season to help United move seven points clear of City at the top of the table.
Mancini also expressed his unhappiness at losing out in the battle to sign Van Persie, but Tevez insists the current squad can prove they are just as prolific in front of goal.
"Those words were a motivation for the strikers," the Argentinian told several newspapers.
"We know that we need to carry on fighting. United lost some games last season and we were back on track, so we will keep doing our job.
"There's a long way to go and a lot of games to play. 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.
"We want to keep winning, to keep fighting for the title. I will try to help us to compete on both fronts, the Premier League and FA Cup, and try to win both."
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