Losing the first leg of this last-32 tie 2-1 in Denmark was one thing, but Pione Sisto's fine solo effort left United facing one of their most humiliating European exits ever.
Van Gaal's men rallied rather than wilted under the Old Trafford floodlights, though, with Nikolay Bodurov's first-half own goal followed up after the break by a brace from teenage debutant Marcus Rashford.
Ander Herrera and Memphis Depay added extra gloss either side of Andre Romer's red card to make it 5-1, but it was the 18-year-old Rashford - thrown in after Anthony Martial's warm-up injury - that grabbed the headlines on a night when fellow teenager Joe Riley also made his first start.
"I think it is a fantastic performance because we started so well and created so many chances," United boss Van Gaal said.
"In spite of that, they scored out of the first time they crossed the middle line.
"Then maybe you get a decline of confidence but, no, the spirit was so high in this match.
"We scored the equaliser, we missed a penalty and then still we continued with attacking football, with the spirit to win, and that is not easy.
"Now you think it's easy after 5-1, but it was not easy. They were well organised and the spirit was there and a lot players reached a higher level.
"It is a mixture (that brought that spirit) - it's not that or that.
"We have done the preparation as usual so it's only the guts of the players.
"I have given also great compliments to the youngsters because that's not easy for Marcus Rashford or Joe Riley to play their debut in a Europa League match.
"It's a higher level and the pressure that you have to win, so they have shown a fantastic level.
"But, of course, a lot of players have shown a fantastic level otherwise you cannot win 5-1."
United's reliance on youth is borne out of necessity due to the club's injury crisis, although Rashford had been so far down the pecking order that his name did not even appear on the back of the matchday programme.
Midtjylland boss Jess Thorup said his debut was "almost perfect", but Van Gaal was keen not to get carried away.
"I've said already a lot of times that that is fantastic but you have to be consistent," he said.
"We are looking for consistent strikers and there are not so many on this earth, but he gave a brilliant performance.
"I didn't have another option, so it was easy. He was there on the bench because he was the natural substitute of Martial."
Source: PA