David Moyes’ men are on a run of three successive victories but their last two home games in Premier League action were back-to-back defeats against Everton and Newcastle.
Evra says his side have to show their character in order to avoid further damaging defeats and criticism from the club’s supporters.
"We have had more trouble at Old Trafford and that is where we have to show our character," he told reporters.
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"When we lost against Everton and in the game against Newcastle, it was obvious we looked a little bit worried. The crowd were not happy sometimes.
"We have to deal with that because we need the fans. If they want to criticise us, we deserve that because when you play for Manchester United, you have to play with pressure."
United’s most recent of the run of three victories was the 2-0 win over Stoke City in the Capital One Cup quarter-final on Wednesday night, in which Evra netted a rare goal.
The 32-year-old defender admits his right-footed strike was fortunate but said he was delighted with his side’s performance.
"My goal was an accident - normally I only use my right foot for getting on the bus!
"I was really pleased to beat Stoke. The conditions were not easy, but you could feel the Manchester United spirit coming back.
"To win 2-0 at Stoke it has to be a great performance. When we lost against Everton and Newcastle it was a massive blow but we have reacted well with three wins in a row.
"Now we have to make sure we win on Saturday. That is my concern and my focus.
"Of course we need points - I wouldn't lie and say anything else. You can talk a lot but what counts is how you act on the pitch.
"I want to get another unbeaten run going, but this time we do not want to slip back again. It is too painful for us, for the staff, for the fans. We have to make sure we keep winning games."