United infamously threw away an eight-point advantage last season to hand the title to Manchester City on goal difference.
Asked if United would slip up again, Evra said: "I think Ferguson is going to sack everyone if we did that. No, I'm serious.
"It would not be funny, for the fans, for the players, for everyone.
"I remember what happened last year. We were eight points clear and, in the end, we lost the league."
United moved six points clear of City after Sunday's dramatic 3-2 win at the Etihad.
But Evra, 31, says that result will mean nothing if they slip up at home to Sunderland on Saturday.
The French defender added: "A six-point lead... the league is not finished yet, there is a long way to go.
"But I really mean we have to make sure we are ready for Sunderland."