United's travelling support sang their displeasure as the 2-1 loss on Thursday evening dented the team's best hope of returning to the Champions League next season.
Midtjylland were Danish champions last year but had won just one of their previous ten fixtures and not played a competitive match since December.
Van Gaal, whose team trail fourth-placed Manchester City by six points in the Premier League, had played up United's “positive” start to the year after they came through their first four games of 2016 undefeated.
But United have now recorded just two wins in six since they beat Liverpool on Jan. 17, increasing the pressure on their manager once again.
“The fans can criticise. They are disappointed, like we are,” the Dutchman said when told what supporters had been singing. “They can do because when you see the second half maybe they are right. We have to improve and then the fans shall support us again.”
With keeper David de Gea injuring a knee during the warm-up to join a lengthy casualty list that includes captain Wayne Rooney, Van Gaal cited injuries as a factor in the defeat.
“It is difficult to cope with such a list of injured players,” he said.
That defence did not go down well at home.
Columnists at the Manchester Evening News described the defeat as a “new low” and called for Van Gaal to be sacked, while many irate fans took to Twitter.
“Please, please just sack Van Gaal he is the worst thing that has ever happened at United,” one user tweeted.
“The level of @ManUtd's uselessness is unmatched,” said another.
Original source: Irate fans turn on Man United