The centre-back, who gave his side the lead at Old Trafford, believes the Red Devils are capable of getting a result in Bavaria
The Serb headed United into an unlikely lead at Old Trafford in the first leg on Tuesday night before Bastian Schweinsteiger equalised to leave the tie finely poised with 90 minutes left to play.
And, despite David Moyes's men still being underdogs to go through to the semi-final, Vidic believes that their pace in attacking areas will cause problems for Bayern's defence.
Speaking to ITV Sport after the game he said: "It was a tough game. We had a good result at 1-0, we felt we were in good positions.
"We were solid but one mistake we were punished and they showed what a good team they are. They had a lot of possession tonight. We accept it was going to be most of the game in our half but we tried to go on the counter attack.
"In the Champions League we've played quite well. Other games I think we've defended well, we've played as a team and we're a bigger threat on the counter attack. Against Liverpool it was a different game. They let us have the ball and they played on the counter attack. That's why we struggled.
"It will be the same game [in the second leg at the Allianz Arena]. They're going to have a lot of possession at their ground. We have to keep the shape, stick together and with the players up front with pace I think we can hurt them."