Evra was captain for United's season-saving second-leg win against Olympiakos in the Champions League last Wednesday.
He told the Daily Star Sunday: "It was really tense in the dressing room before that match.
"I said to all my team-mates, 'Tonight, we have to play for the people we love - for the United family and not for the people who criticise us'.
"We had to give back after the Liverpool game. Losing 3-0 at home and the fans were still singing.
"When I got home I was really sad but at the same time I was happy because we have the best fans in the world. In my head, I was saying I couldn't wait for the match against Olympiakos to give them back what they gave to us.
"A lot of people say you need the fans because when we do the job on the pitch, they'll always be behind us.
"That's why I want good times for all the Manchester United fans.
"I said before the Champions League game that I want the fans to be proud of us and we ought to say thanks to God to be able to play in the Man United jersey.
"Maybe people will say I'm too old school but when you play with spirit, you can do big things.
"I was so happy for the players, for the fans and for the new staff."
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