It followed a 4-2 first-leg victory in Denmark where the club's fans were praised by the local police.
The Denmark press had their say on the return in Glasgow with Politiken not holding back in their assessment of the tie.
They ran with the headline: "FCM finishes in Europe after humiliation against Rangers FC".
The Scottish side's dominance "at the legendary Ibrox Stadium" was noted by the paper who felt Midtjylland's "midfielders were clearly defeated".
Alfredo Morelos and Sheyi Ojo combined for all three goals with Bold.dk labelling the duo "pure poison for the FCM defence".
Jyllands-Posten thought "FCM seemed strangely unengaged for much of the match and only woke up in the last quarter" while tabloid B.T. felt that they had actually started well before Alfredo Morelos netted in the 14th minute.
"FCM got off to a good start in Glasgow," the paper said, "but after a quarter, things went wrong."
Even the club itself recognised the task which was required in Govan.
The webiste report read: "FC Midtjylland on Thursday night hunted down the miracle in front of 47,000 spectators at Ibrox Stadium in Glasgow, with the hosts having a 4-2 win from the first show in the third qualifying round of the Europa League."
Even when the side got back into the game in the final period it was noted that that was partly down to Rangers.
"The Rangers team pulled the handbrake sharply in the second half, allowing FCM to get more in the game, which Evander used to reduce by one."
Magnanimous as ever, FC Midtjylland tweeted: "Congratulations on the deserved victory, and good luck in the play-offs."
After the game former Celtic centre-back Erik Sviatchenko lamented mistakes in both the defensive and attacking thirds but did admit that they met a strong team.
When walking off the pitch, Rangers boss Steven Gerrard made a “zip it” gesture to the FCM captain.
“I just wished him all the best for the remainder of the season,” Gerrard said. “He had obviously been speaking quite a lot through the media over where he is from. So it was just a little send-off for him.”
Looking at the bigger picture the English-language outlet Copenhagen Post put it bluntly in their online headline: "Miserable European week for Danish football".
Copenhagen lost in the third round of Champions League qualifying, while Brondby lost 7-3 on aggregate to Braga in the Europa League. Esbjerg had already fallen.