City and Liverpool are United's biggest rivals and Evra knows there cannot be a repeat of what happened a week ago.
The defender, 32, said: "The fans don't want to be hurt again against our neighbours.
"If you lose 3-0 to Liverpool, you think the fans will boo you. I think we deserved that - it would have been no surprise.
"But I was in shock because they were still singing until the last second. You have to make sure when people give you something, you have to give back. It's payback.
"But, personally, I'm never happy to lose against Liverpool. The way we lost the game hurt me.
"I don't think we fought enough and that's why I was really hurt."
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