United travel to the Allianz Arena on Wednesday for a second-leg showdown with the reigning European champions knowing they must score following their 1-1 draw at Old Trafford.
Although the defending Premier League champions sit a lowly sixth and are unable to retain their league crown, full-back Evra believes their European form has been a different matter.
Furthermore, Evra admits the Manchester United dressing is much more focused on a trip to Germany than domestic affairs.
"You have to believe and, to be fair, this season we have played not so bad in the Champions League," Evra told reporters after United's 4-0 victory over Newcastle.
"We are confident and it looks like we are all up for it more than the league and in the cup.
"I know it is not professional to say that but it is the truth.
"We look more on it, we look more like we have the Man United spirit when we play in the Champions League."
Victory over Newcastle at the weekend was a 10th away win of the season for David Moyes' side and Evra expects United to take heart from their success on the road when they come toe-to-toe with Bayern, who suffered a first league defeat in 18 months against Augsburg on Saturday.
"I think everyone has noticed that we play much better away," he added.
"It is frustrating because maybe at Old Trafford it is different, it is a different pressure.
"We have good away form so let's try against Bayern away and make sure we give everything."
The Frenchman also dreams of emulating Chelsea's dramatic Champions League triumph over the same opponent in 2012, when they also finished sixth in the Premier League.
"It was funny because all season reminded me of the Chelsea season they won the Champions League when they were not playing well in the league," he recalled.
"I am not saying we are going to do the same but sometimes you have to be positive, so why not?
"Of course it is unusual for us to say we can save our season in one game. Now we must make sure the fans will be proud for the second leg against Bayern."