Having started slowly at Carrow Road, the Reds came to life after the break with Danny Welbeck's effort giving David Moyes' men a fourth consecutive league win.
Evra was delighted to see United's good run of form continue, but says his side shouldn't get carried away with recent results.
He told MUTV: “It’s a massive win. Norwich played very well and they should have scored a few goals in the first half, but I think the lads deserve plenty of credit. It’s never easy to play two games on the road like that, but the most important thing is the three points.
“I’m just looking at the present [moment in time]. The team is now playing better, we have that winning mentality and United spirit which was missing at the start of the season. I can see that our hunger has come back, so I’m confident, but I don’t want to talk about the title. I just want to talk about the next game, Tottenham at home [on Wednesday]. We need to make sure that we win, and that we keep the momentum going."
The defender was also full of praise for Welbeck after the game, insisting that his winning goal was vital in the absence of injured duo Wayne Rooney and Robin van Persie.