Goals from James McCarthy, John Stones and Kevin Mirallas at Goodison Park left United anxiously looking over their shoulders at fifth-placed Liverpool as they aim for the top four finish that will bring Champions League football to Old Trafford next season.
Afterwards, van Gaal said he had seen warning signs even before kick-off that his players were not at their best.
“I think so, yes,” said the Dutch manager when asked if this reverse was the most disappointing performance of his United reign.
“It was the first time that I see that our motivation, inspiration, aggression was not as high as the opponent.
“I already had the feeling, as did my colleagues (coaches) Ryan Giggs and Albert Stuivenberg, because warming up today was not as good as usual.
“Then you say that in the last minute before kick-off, you hope that you can recover that and stimulate your players but then it’s too late.”
Van Gaal added: “Because we are playing so well the last six or seven games, the players think ok, it will come.
“But you need the inspiration and motivation and aggression to win the second balls and fight until the end. I have said so many times this season that they have fought until the end and what more can a manager demand,” van Gaal explained.
– Given light to Liverpool –
Liverpool trail United by seven points but have a game in hand and will have played two matches before United next take the field — against West Bromwich Albion on Saturday — meaning van Gaal’s side may only have a one-point cushion by the time they kick-off.
“I know that,” he said. “I have said that to the players — you have given light to your opponents.
“I hope it won’t happen again. But, as a coach, I know that it will happen again (some time),” added a rueful van Gaal.
Sunday’s reverse also represented a miserable return to Goodison for former Everton midfielder Marouane Fellaini who missed a glorious chance to equalise, was booked for a foul on Ross Barkley and then substituted at half-time, in part to avoid a dismissal.
“There were several reasons I brought him off,” said van Gaal. “The first was he was booked and I found that the Everton players provoked him and I was not so sure that he would end the match.
“Also, because of the score at half-time, but of course I could have changed even more players.”
Everton manager Roberto Martinez, whose side have won five and drawn one of their last six league games, was delighted with the Toffees’ latest performance.
“I thought we were the better side in every department and well worth the clean sheet and well worth the three points,” said Martinez, whose team are now in the top half of the Premier League table after being knocked out of the Europa League by Dynamo Kiev.
“We’ve learnt some tough lessons this season but today we performed in a very strong manner,” Martinez said.
“It’s been a big difference, after the amount of time we had to cope with the demands of Europe, and it was not until we got to the end of January that we found the right mentality to cope.
“As a team we’re developing but the know-how and mentality you need, you can’t learn unless you go through the experience.”