United were crushed at Old Trafford losing 6-1 to their arch rivals, whilst Vincent Kompany's header at the Etihad Stadium in April saw Roberto Mancini's side win 1-0 in what was billed as the one of the biggest games in Premier League history.
The defeats still hurt those at Old Trafford and the 28-year-old Scot knows that only victories will do this time around.
"Last season we lost twice against City and we lost the league so that was a major factor in that," he told the Manchester Evening News.
"We don’t want to give them any advantage by beating us. It is about time we got a result against them."
United go into the game on Sunday on the back of a 4-3 victory over Reading, whilst City drew 1-1 at home to Everton leaving the Red Devils three points clear at the top of the league.
After the game on Saturday, Wayne Rooney and Sir Alex Ferguson were critical of United's defending in recent weeks and Fletcher believes they have to be aware when playing City.
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"Defending is becoming a concern. At set pieces it is individual mistakes that we can try and sort out. The first goal against Reading was a fantastic finish but we cannot keep conceding these goals.
"We are talking about it, looking at it and trying to put it right but I think the biggest thing is that we keep coming back.
"I know we keep saying it but it would be a lot more disastrous if we didn't. We do keep responding and that is a good attribute to have.
"People can talk about the goals we are giving away and we are concerned and we don’t want it to happen but we know if we do go behind we have ability and belief to know we can comeback."