Wayne Rooney's 78th-minute strike - the visitors' only shot on target at Anfield - settled a game low on quality and chances.
It left United within seven points of leaders Arsenal and Van Gaal has not ruled out a late charge for the summit
"We have a lot of matches still to go," said the Dutchman.
"We started 2016 very good with a lot of wins and I think this game will give a big boost to the players and the fans, and everyone in the environment of Manchester United.
"We have to continue, which is not so easy
We have seen that today but we can do it because we show every week we can do it."
Asked whether it was his best day of the season, Van Gaal added: "No, I don't think so
You have to see it always in perspective.
"It is a fantastic win for the fans, for me and the players and it will give us a boost, and maybe in that perspective you are right.
"There are matches we have played much better than today, and in that perspective I can't say it is a good day because Liverpool were the better team in the first half and normally we are dominating games.
"I have to admit we survived the first half because Liverpool were more aggressive, we could not create anything.
"They have created in the first half three chances and that was surviving, but to beat Liverpool is always important.
"When I see this game then I think we can still improve but it was still good enough to win at Liverpool away."
The fact United were able to leave Anfield with three points was largely down to David de Gea, who was by far the busier goalkeeper.
However, although the Spain international was named man of the match, Van Gaal saw nothing but De Gea's usual high standards.
"He is always reaching a very high level so I am very happy, but I cannot say that today he has done a lot," he said.
"He has stopped the balls that he had to stop
Maybe the one with one hand (from Emre Can in the second half), maybe but I think he has to save it
I think a goalkeeper has to do it.
"I demand it and I demand it also of the players
That is why he is playing for Manchester United."
Liverpool manager Jurgen Klopp cut a frustrated figure after seeing his side dominate possession and create more chances only to be undone by their Achilles heel of conceding from a set-piece.
"It's really bad; it's a derby and in a derby you only have one job to do: you have to win it
That's the only possibility to be satisfied after the game," he said.
"United at this moment will be happy
You can talk about their performance and it wasn't that good but they won so they are really happy.
"We played better but feel frustrated because there were many things that were good, but our finishing was not good otherwise we would have scored a goal.
"Set-play was not good defending but it was unlucky because we had changed a few positions moments before.
"But three mistakes around the goal were too much against a team of the quality of Manchester United.
"In this moment it is only frustrating, which is how it should be."
Source : PA