United pulled clear of defending champions and cross-town rivals Manchester City with a 3-2 win in a tempestuous derby at the Etihad Stadium on Sunday.
Last season, City capitalised to take the title when United let an eight-point lead slip over the final six games but Evra said there was no chance of a repeat in 2013.
"I think Ferguson is going to sack everyone if we did that," the French left-back was quoted as saying in a number of British newspapers on Tuesday. "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."