The Premier League side lost David de Gea to an injury in the warm-up and struggled to contain the hosts in the early exchanges of the last-32 first leg.
Man United gradually improved and took the lead in the 37th minute through Memphis Depay, but goals from Pione Sisto and Paul Onuachu saw Midtjylland secure an advantage ahead of the second leg next week.
"When you start a game and your goalkeeper is No.14, you are not starting like usual. A lot of things are happening in the heads of the players," Van Gaal told BT Sport. "In the first 10, 15 minutes we were not so good. We improved and scored, but then it is too much.
"The second half we do not win any second balls. You cannot afford to concede a second goal, but we could have scored. Jesse Lingard had two remarkable chances. It is the law of Murphy."
Van Gaal, however, is confident that his team will win the return match at Old Trafford next week and the Dutchman also revealed that De Gea pulled up with a knee problem before the match.
"We were not very organised. We have the chance to beat them at home and I think we can do that. De Gea has a knee problem so we have to investigate tomorrow," Van Gaal added.
Man United will return to action in the fifth round of the FA Cup away to Shrewsbury Town on Monday night.