It was a result which saw the Danes progress to the Champions League qualifying third round where they will come up against Dutch giants PSV, while the Parkhead side drop into the Europa League where they will face Czech side Jablonec.
The Danish press weren’t impressed with what they saw of Celtic.
Ange Postecoglou’s men were constantly referred to as a big club but as Carsten Godtfredsen wrote in Politiken: they are not a “dreaded opponent”.
"The ugly point fact is the kind that really hurts a club like Celtic, because the green stripes from Glasgow have a very proud football history,” he said of the club’s 25 points difference to Rangers.
“It says a bit that FC Midtjylland should have a good chance in the game, because Celtic today is, seen through European eyes, a good distance from the level that once made the team a dreaded opponent.”
Of the game, Berlingske noted it was a “poor first half, the two teams took turns dominating the game in the middle of the field, without it really carrying anything with it”.
Callum McGregor’s stunning goal, however, was described as a “pearl” by Politikenafter “chest taming” the ball.
Former Celtic defender Erik Sviatchenko felt Midtjylland were the better side in extra-time.
"In the extended playing time, I think they were completely gone, and there I really felt that we dominated," he said.
Manager Bo Henriksen added: “I think it is completely deserved and completely fair that we won. It was a clever, cleverly played football match.”