Serbia international believes losing to the Red Devils' cross-town rivals was the result of a momentary lapse of concentration, but hopes to right the wrongs on Tyneside
Roberto Mancini's men took the lead through a goal from Yaya Toure, who capitalised on an error by Michael Carrick. City were given a further boost when they were handed a numerical advantage following the dismissal of Paul Scholes for a rash challenge on Pablo Zabaleta.
The defeat prevented United from realising their treble dream, though they remain in contention for the Premier League and Champions League crowns.
Now the Serbia international has called on the squad to put the defeat behind them with a good performance against Alan Pardew's men.
"We lost a moment's concentration and conceded a goal in the process. Then when you go down to 10 men it is difficult to get many chances against City," Vidic told reporters.
"In the first half we played some good football. We had two or three chances but didn't take them.
"Then in the second half when we lost a goal, it was difficult to take. Obviously when you are playing with 10 men you are chasing the game.
"We have to think about the next game against Newcastle [on Tuesday], especially after losing the semi-final to City. It will be a very important game for us.
"We still have many games to play. Obviously the next one is the most important one. We have to play the best we can and win that game."