A first-half penalty from Daniel Sturridge was followed by a decisive second from Roberto Firmino 17 minutes from time but the 2-0 scoreline would have been much worse had it not been for the heroics of goalkeeper David de Gea who made four or five decent saves.
A UEFA Europa League exit to their arch-rivals next week would put Van Gaal under even greater scrutiny, even with his side just three points off fourth place in the Premier League and still in the FA Cup.
To avoid that he needs to devise a game plan to counter Liverpool's high-tempo pressing style which did for them at Anfield.
"We did not cope with the high pressure of Liverpool. The pressure is not from the crowd," said the Dutchman.
"We had expected that and for me it was a surprise we did not cope with it because they did it at their home match this year.
"That raised the atmosphere in the stadium and they created big chances but we had a very good goalkeeper and because of that we were in the match."
United's performance was criticised by former players Rio Ferdinand and Paul Scholes as being 'disjointed' and 'shambolic'.
However, a tetchy Van Gaal rejected their opinions.
"Is it important what Rio Ferdinand is saying, is that important to you? You don't give your opinion and then you give Rio Ferdinand's opinion - that is very strong of you," he added.
"Of course Liverpool were the better team in the first half but in second half we did a better match than before that.
"I don't think we were very creative in the third and fourth phase but it is also the defence of Liverpool and you can give credit for that to Liverpool.
"We have to improve a lot to create more goals."
Van Gaal also had issues with both goals they conceded.
He said: "We get a cheap penalty and that was 1-0. Henderson was in an offside position (for the second goal) and when you are so sharp you can see the foul has been made by Memphis in the area (for the penalty) you have to see also when it is offside."
He also insisted he was not aware of an apparent Marouane Fellaini elbow on Emre Can in the closing moments.
"I haven't seen it but I think also I have to say Fellaini was one of the best players on the pitch and I am very sorry when he makes a mistake like that," he said.