Robin Van Persie broke City hearts and grabbed first bragging rights of the season as he curled in a free-kick deep into injury time.
And Evra said: "I don't know why we like to excite in the game like this and win in the last minute but in the end we win and that's the most important thing.
"It's a derby and when you play a derby it's for winning not just for playing. We couldn't go away with only a draw.
"It's three massive points today. But there's a long way to go, I remember last year we went eight points clear and in the end we lost the league.
"But psychologically it was really important to win against City but it's not done yet."