The Red Devils dealt a potentially decisive blow to Tottenham’s top-four hopes after goals from Marouane Fellaini, Michael Carrick and Wayne Rooney in the first half at Old Trafford.
United are five points clear of their nearest rivals Liverpool ahead of the 20-time English champions’ trip to Anfield in the Premier League next Sunday.
Van Gaal, who agreed a deal to become United’s permanent manager last May, urged his Red Devils side to stay focused despite moving to within two points of second-placed Manchester City.
“We have to go step by step, it’s a rat race,” Van Gaal told his post-match media conference.
“We are two points away from second place, but first are eight points and that is too far away. We have to go step-by-step and the next game is against Liverpool.
“If I’m right, Manchester United haven’t won many at Liverpool.”
United bounced back from their FA Cup disappointment after the Red Devils suffered a surprise 2-1 defeat by Arsenal in the quarter-final at Old Trafford last Monday.
United have just won two of their last seven games away from home in the Premier League ahead of their trip to Anfield.
The Red Devils lost 1-0 on Merseyside last season after Daniel Sturridge scored a fourth-minute winner in September 2013.
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