Roberto Mancini's men lost 2-0 at Everton in the lunchtime kick-off when goals from Leon Osman and Nikica Jelavic put a massive dent in their title aspirations, and Sir Alex Ferguson's side capitalised with a nervy win later in the day.
While 31-year-old club captain Vidic acknowledges there is a "big gap" between the Manchester rivals with nine games left to play, he maintains his side must hold their nerve after collapsing last season to let City back in the title race.
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"If you look at the 15-point lead, you have to say that it is a big gap and we shouldn't let anything change. We have the title in our hands but we have games still to play and some especially tough away games that are traditionally hard for us. Nothing is finished yet, but we're in a good position.
"Sometimes you can feel the fans in the stands getting nervous because they think about last season. I don't think we should allow that to happen again," he added. "We are in a good position now. We should relax and enjoy playing football. It is a good time for us."
United still have difficult games against City, Chelsea and Arsenal but can clinch the title by collecting 13 points from their remaining nine games - meaning maximum points and then a point against Aston Villa on 22 April would seal the trophy.