The Red Devils will clinch the Premier League title if they can beat Aston Villa at Old Trafford on Monday night and Evra feels the plaudits will be thoroughly deserved once they secure their 20th top flight trophy.
"People want to see Manchester United fall down," said Evra. "In the seven years I have been here, it has always been the same.
"When you lose one game it is like the end of the world. If you don't accept this pressure, you can't play for Manchester United.
"It is right that in the beginning of the season, we were not doing well, we always had to come back. But we did keep winning. People forget we are a marathon team. The league is not a sprint."
He added: "Everyone said City were better than us, that they had played the best football.
"I admit we didn't play well. But in the end we finished on the same points.
"In my last interview I said if Manchester United got the consistency back, maybe we can win the league by 10 points.
"For the moment I am wrong. It is 13 points. I didn't say it to make the fans, or the staff or my teammates happy. I said it because it is the truth."