United beat Manchester City 3-2 at the Etihad Stadium on Sunday to move six points clear at the top of the table.
Last season United let an eight-point lead slip in the final six games and Evra is determined to avoid a repeat.
"I think Ferguson is going to sack everyone if we did that," Evra said. "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, so a six-point lead means the league is not finished yet.
"There is a long way to go, but I really mean now we have to make sure we are ready for Sunderland on Saturday."
Evra also praised the impact of Robin van Persie since his arrival from Arsenal and said an August afternoon in Southampton, during which he scored a hat-trick but also missed a penalty, was revealing.
"Robin is perfect for Manchester United," added Evra. "When he scored the hat-trick at Southampton he also missed a penalty.
"The first thing he said when he came back to the dressing room was that he was really sorry for missing the penalty. That shows the hunger, humility and personality he has to win trophies.
"He is not just scoring for himself. He really wants the team to win something."
Wayne Rooney's contribution had been overshadowed by Van Persie's exploits but four goals in a week have taken his season's tally to seven.
Evra continued: "A lot of people criticised Wayne at the beginning of the season, asking why he didn't score so many goals.
"Last week he scored two goals. (Sunday) he got two again. He is a really important player for us."
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