The Red Devils’ victory over rivals Manchester City on Sunday saw them open up a six-point gap over their neighbours at the top of the table.
Evra, though, is wary of how any carelessness can see such leads disappear, with City having chased down an eight-point deficit between the two sides in the final six matches of last season to seal a famous league win.
When asked about last year’s title race, the 31-year-old told reporters: "I think Ferguson is going to sack everyone if we did that [again].
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"I remember what happened. We were eight points clear and in the end we lost the league."
Turning his thoughts to Sunday’s derby win, the Frenchman was keen to emphasise the significance of a victory as visitors to the Etihad Stadium, as well as the psychological implications that the result could have on the remainder of the season.
"It was more important to win at City and give a sign out to them," he added.
"We also broke their record at home. Psychologically, it was really important to win against City."