With the two sides level on points, United must rely on relegation-threatened QPR to deny City all three points at the Etihad Stadium.
But City have only dropped two points at home all season, so Evra admits it is a long shot, but says all United can do is "believe".
"We cannot think about what Manchester City are doing," Evra told reporters.
"We just have to make sure we win.The Sunderland game isn't easy but if we score first then maybe the City fans in the stadium will start to get nervous.
"When you are nervous then you can rush things and you don't do things as well as you'd like."
The Frenchman said that manager Sir Alex Ferguson is hurting most after United's 4-4 draw at Old Trafford against Everton opened the door for Roberto Mancini's men to take pole position in the race for the title.
"It hurts the manager a lot when we lose a game, more than it used to," said the France defender.
"That shows you the character and the personality he has to always win.
"If we don't win the league it will hurt a lot of people, but the first person it will hurt will be the manager."
Evra finished by committing himself to the United cause whatever the outcome on Sunday, insisting he will continue to give everything to the club.
"We always bounce back," he said.
"I trust everyone working for this club and I would never turn my back on Manchester United.
"You have to have belief. But maybe, if we don't win, everyone - including myself - will say that 'I have to do much better' if we want to win the league again.
"So we will try and rebuild something that's stronger and try and win every competition next season.
"That's the United way - every year we start the season wanting to win every trophy.
"We need to make sure that next year we give everything to do that."