The Red Devils go into the match with a 2-0 deficit to overturn following the first leg between the two sides in Greece three weeks ago.
With the club having endured an inconsistent season under the management of David Moyes, Evra has vowed that he and his teammates will "fight" to appease the fans at Old Trafford.
"When you win, you win together and when you lose, you lose together. It's been a difficult season for everyone because we're not used to losing. We know we had a bad game in the first leg. Even a three-year-old Manchester United fan would be hurting by our performance, but in life you have a second chance and we will have one tomorrow night. We will fight and make sure all the fans will be proud of us after the game," the Frenchman told reporters.
United have won both of their previous home matches against Olympiacos.