"I remember what happened last year," said Evra. "We were eight points clear and in the end we lost the league.
"No, this match was more important to win at City and give a sign out to them. We also broke their record at home, which was really important.
"Psychologically, it was really important to win against City. I think Ferguson is going to sack everyone if we let this lead slip. No, I'm serious. It would not be funny, for the fans, for the players, for everyone.
"A six-point lead - 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."
The 31-year-old, whom Paris St-Germain have aspirations to buy with a £5million January offer, believes Ferguson's squad have learnt last season's lessons - when they were too fixated on City and played overly defensively in a 1-0 defeat at the Etihad Stadium.
"This was a good win because we won again like the Man United way," Evra said.
"We're very happy because we stuck to the plan. Last year we talked a lot about City before the game but this year we just talked about us.
"It was about us - just to put some pressure on them and don't let them play and when we get the ball to make sure we score."
Of Wayne Rooney, blossoming as an advanced midfielder and United's star performer in the derby, Evra was equally ebullient.
"At the beginning of the season a lot of people were criticising Wayne, which was normal because Robin van Persie joined us and is doing great," said Evra.
"But you can't forget Wayne and he just proved it. He scored two goals in the last game against Reading and he's scored another two goals again against City.
"In the big games you need your big players and Wayne is one of them."
The spirit of United was evident again in Sunday's comeback, the French defender reflected.
"We've done that a lot this year," he said.
"I know people criticise us for conceding goals but the most important thing is to win games and that's what we are doing now.
"I know we have to defend better but in the end we showed the character."
Evra was unconcerned by the coin which hit Rio Ferdinand.
"He was just hit by a coin thrown by a fan but Rio is okay. He is a strong lad," he added.
It is unclear how long City defender Vincent Kompany's hamstring injury will keep him out of action for but it may be several weeks - enough to rule out any prospect of Joleon Lescott being allowed to leave on a loan deal in January.
Although Kolo Touré was unimpressive when he replaced Kompany on Sunday, the Ivorian's departure to next month's African Cup of Nations will also leave City a defender down.