England defender Harry Maguire scored the only goal of the game in the 72nd minute.
The win was an important result for the Red Devils as it was their first victory in the Champions League this season.
They had earlier lost to 4-3 German Champions Bayern Munich on September 20 and 3-2 to Turkish Super Lig side Galatasaray on October 3.
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United have also been out of form in the Premier League this campaign as they are out of the top seven spots.
In an interview with MUTV, Ten Hag said the penalty they conceded in the 97th minute was a soft penalty.
Im very pleased, it was a narrow escape as we needed to win, Ten Hag said.
We worked very hard to get that win. It was a poor first half but then, to come into the game, to score that goal and then concede a soft penalty. So it was important as we needed a win today. I think we created some chances but we didnt take them.
It is good that a defender is coming forward and scoring a brilliant goal, with a great assist from Christian Eriksen. I think we should have scored more but also we could have conceded more goals. So 1-0 and Im happy with it, a clean sheet and we scored.
Its always going to be complicated. It belongs to the DNA of Manchester United. It was a crazy game. A nervous game for us in the end. I dont have an influence on that (the penalty) and you feel bad in such moments because wed worked so hard for the win and then we concede the penalty and then it gives Andre the platform to show his skill. It was a great save.
The last encounter between the teams was in the 2006/07 edition of the Champions League. Manchester United won the first leg 3-0 while FC Coppenhagen triumphed 1-0 in the second leg.
The Red Devils are third place in Group A of the Champions League with three points after three games.
United have won the Champions League three times (1967/68, 1998/99, 2007/08).
They are eighth on the Premier League table with 15 points after nine games in the division.
FC Coppenhagen are in last position in the Champions League with one point after matchday three.
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