Patrice Evra claims Manchester United's players are being driven on by the fear that Sir Alex Ferguson will "sack" the entire team if they were to repeat last season and allow an eight-point lead over Manchester City to slip.

United ended their fiercest rivals' 37-game unbeaten home league run with Sunday's 3-2 win on a tumultuous afternoon at the Etihad Stadium. This took their advantage over the champions to six points. In last season's title race United led City by eight points on 10 April with only six games remaining.

Asked if the experience of allowing Roberto Mancini's team to win the championship from that position means United will not let the current lead slip, 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.

"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 for Sunderland [on Saturday].

"I remember what happened last year. We were eight points clear and in the end we lost the league. No, [it] 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."

Last season United lost both derbies on a 7-1 aggregate, including a 6-1 defeat at Old Trafford in the first encounter.

"Last year we talked a lot about City before the game but this year we just talked about us," Evra said. "It was about us – to put some pressure on them and don't let them play, and when we get the ball to make sure we score a goal. That's what we did in the first half. In the second half they put a lot of pressure on us and hit back. I thought it was similar to the Chelsea game in that way [United won 3-2 in October] but in the end we won and that was the most important thing."

Against City Wayne Rooney scored twice in the first half before Yaya Touré and Pablo Zabaleta drew Mancini's side level after the interval. A 92nd-minute winner from a Robin van Persie free-kick preceded controversial scenes which included Rio Ferdinand being struck by a coin thrown by a City fan, then Joe Hart having to intercept a different home supporter who invaded the pitch and approached the United defender.

Evra, who is under contract until the summer of 2014, was again proud of United's fighting spirit. "We did that against Chelsea, we've done that a lot this year," the captain 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.

"We have to defend better but in the end we showed the character and when you win like this, it's the Manchester United way. It was a good win … We're very happy because we stuck to the plan."

Of City's prospects of retaining the title, their defender Zabaleta said: "We were disappointed because we've lost the most important game and now we are six points behind them.

"Now we have to be positive – there is a long way to go. We showed last season we were eight points behind United and we got them. We have to keep working hard."