Anthony Martial scored the only goal - from one of just two United shots on target - as Van Gaal's side edged the Toffees 1-0 in a tame Barclays Premier League contest at Old Trafford on Sunday.
Van Gaal accepted United were below par but the result lifted them back within a point of fourth-placed Manchester City in the battle for Champions League places.
"I said in the dressing room that it was very important to win, otherwise the victory against City was worthless," Van Gaal said.
"We keep in touch with City, one point behind
We keep in touch with Arsenal, five points behind
We now have to play Tottenham - not an easy match - but normally we are playing very well against the top teams
If we continue like that I shall be very happy."
United had the best chance of a goalless first half when a Martial shot was deflected narrowly wide
The breakthrough came after 53 minutes when substitute full-back Tim Fosu-Mensah, on for the off-the-pace Marcos Rojo, took advantage of slack defending to tee up Martial.
Everton, who held their own in an evenly-fought contest, almost responded immediately as Phil Jagielka headed against the bar and the same player was later denied by David de Gea but United held on.
The visitors also had some bright moments in the first half as Gerard Deulofeu tormented Rojo and Van Gaal put the Argentinian defender's poor display down to the after-effects of international duty.
Van Gaal said: "I think Rojo had a problem with his jet lag, otherwise I cannot imagine (why he struggled)
So, I changed him."
Defeat left Everton 12th in the table and the frustration of their fans at their perceived under-achievement was evident at the final whistle as they booed their own team.
Manager Roberto Martinez recognised this and claimed the players were just as disappointed.
The Spaniard said: "We all are (booing)
I think you could hear our boos in the dressing room
It is exactly the same."
But Martinez remained upbeat about his side's prospects, particularly as they have an FA Cup semi-final to look forward to - against either United or West Ham - later this month.
He said: "The frustration we all have is we can see the quality we have in our squad and we can't really gain some sort of momentum.
"But 1984 is the last time we got into the semi-finals of the two domestic cups and this generation (of players) can make us very successful."
Source : PA
Source: PA