Marouane Fellaini, Michael Carrick and Wayne Rooney found the net in a rampant performance - arguably United's best of the season so far.
After losing at Burnley on Saturday, City have fallen further behind Premier League leaders Chelsea and Manuel Pellegrini's men are now in Van Gaal's sights.
When asked whether City had been dragged into the "rat race" - a term Van Gaal uses to describe the fight for the top four - the United boss said: "Of course, because Arsenal is one point behind and we are two points behind.
GETTY
Louis van Gaal sets his sights on catching rivals Manchester City
It is a rat race and we are now two points from the second position
Louis van Gaal
"It is good for us and the fans and the media because you can write a lot of things down.
"We have to go step by step. It is a rat race and we are now two points from the second position."
However, the Dutchman believes the title is as good as gone. "It is too far away," he said, mindful of the fact that United are eight points behind Chelsea having played one more game.
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