The defender admitted the loss at Old Trafford was "painful" and insists his side's next match against Stoke City at the Britannia Stadium will be difficult.
Roberto Mancini's side cut the gap at the top of the Premier League to 12 points after strikes from James Milner and Sergio Aguero sealed a 2-1 win for City at Old Trafford on Monday evening.
"We're really disappointed because we missed the chance to end the title [race] and, of course, we've lost the derby. When you're a Man United player losing to City is painful," Evra told MUTV. "We played much better in the second half and I really believed we could win the game, but the second goal killed our legs. It's a bad night for us.
"We are still 12 points clear though and now we have to win the next game. Since I've been here, I've never lost two games in a row...I heard a lot of people talking about us being 15 points clear and that we didn't deserve to be. But if that's where we are it's because we're working hard. We must make sure we win at Stoke and show we are the best team in England."
United is unbeaten against Stoke in the Premier League, but Evra is anticipating a tough match at the Britannia Stadium, despite Tony Pulis' men going without a Premier League win since Feb. 9.
"It's always a difficult place to go. We have to be ready for the fight. We've always left there with three points in recent years but nothing is going to be easy until the end of the season," he said.
"We have to make sure we win the next game. That is the most important thing. We are still in a great position but we have to take things game by game and not put pressure on ourselves."