Sir Alex Ferguson’s side have fallen behind in 15 of their 23 games this season and shipped three against strugglers Reading last time out in the Premier League.
Although United went on to win the game 4-3, Rafael was hauled off in the first half of the match and believes the whole team have to improve defensively.
When asked if he believed Manchester City could destroy their opponents on Sunday, he told The Guardian: "Of course, yes.
“If we defend like we have done in some games we will be in real trouble against a team like City.
"That's 100% sure. I don't know why we have had problems defending this season. If we work hard in training I'm sure we can learn to defend better.
"In the Premier League Manchester City are doing very well – they just seem to keep going and going. But we just need to concentrate on ourselves.
“It is a big game for us and we need to play at our best level. They have a very good attack with some quality strikers. This will be our biggest test of the season.
“They have two Argentina strikers [Carlos Tevez and Sergio Agüero] and I am from Brazil so that increases the rivalry for me."
After losing the Premier League title to their rivals on goal difference after Sergio Aguero’s dramatic winner against QPR on the last day of last season, Rafael believes the experience has installed a new determination within the squad.
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“We are really determined to make up for losing the title to them last season. The way we lost it [on goal difference, on the final day] made it even harder to accept," he continued.
“This season we are determined to win the title back. I will never forget how I felt that night after we had lost it and that will give us more motivation, definitely.
"We just looked at each other and said: 'How did we lose it by a few goals?' It was hard to take. It took ages to get over it – and it [the pain] is still there."
However, a win on Sunday would move United six points clear of the champions and the full-back says that is huge motivation for his side as they prepare for the short tip to Etihad Stadium.
"The derby is a big game and it is getting more and more important each season," he added.
"It would be very important to build a six-point lead over them before Christmas. That would make them nervous and make it easier for us."