The Premier League leaders are heading for a third round replay with West Ham United on 16th January at Old Trafford after a 2-2 draw on Saturday evening at Upton Park.
And Vidic has revealed Sir Alex Ferguson's squad are determined to end a wait to win the FA Cup which stretches back to 2004.
"We believe it's important," the centre-back told MUTV on Saturday. "We didn't win the trophy for the last eight years and it's a trophy we're looking to win.
"We showed today in how we celebrated the goal, and I'm hoping at home it will be a different game. I think we have a big squad and we can manage to have one more game."
West Ham came within seconds of making Manchester United wait another season for FA Cup glory after taking a 2-1 lead into injury time.
But a splendid Robin van Persie equaliser set up the replay after two James Collins headers had earlier cancelled out Tom Cleverley's opener.
And Vidic said of Van Persie, who had started the game on the bench: "His touch is magnificent and his finishing is top class.
"It's movement from the book, touch from the book, goal from the book. It's something they can show to kids, how to move and finish in the last third.
"He was magnificent for us. We just hope he's going to be in the same form in the end."