Mohamed Salah gave Liverpool the lead in the opening minute of the game with a lucky goal. After he went through on goal, Salah was caught up by a defender, but the ball ricocheted into the net off the Egyptian.
Liverpool had further chances through Diogo Jota and Divock Origi in the first half, but Midtjylland were definitely growing into the game.
In the second half, Midtjylland were fully in the ascendancy and got their chance to score when Anders Dreyer was brought down in the box by Caoimhin Kelleher. Alexander Scholz made no mistake from the spot. Scholz thought he had a second goal a few minutes later but was denied by VAR.
Liverpool were also denied a winner by VAR when Sadio Mane was penalized for a handball after Takumi Minamino had put the ball in the net.
The Reds now go into Monday's Round of 16 draw as one of the seeded teams after winning Group D, with 13 points from six games.
Here's how each player fared for the Reds.
Liverpool Player Ratings vs. FC Midtjylland
Caoimhin Kelleher - 7/10
Kelleher made a couple of excellent saves, particularly one from an Erik Sviatchenko header. He was guilty of conceding the penalty that led to the equalizer, but he was left exposed by those in front of him.
Trent Alexander-Arnold - 5/10
In the larger context of Liverpool's season, this game was important for Alexander-Arnold to get his sharpness back after his return from injury. In his first game as Liverpool captain, he did not put in a great performance and needs a bit more sharpness to get his touch with the long passing back.
Rhys Williams - 6/10
Williams once again put in an assured performance at the heart of the Liverpool defense. He was particularly dominant in the air.
Fabinho - 7/10
Fabinho played only the first half of this game, as he got some much-needed rest ahead of a tough run of Premier League fixtures. He stopped a certain goal off a Sory Kaba header with a superb clearance off the line.
Kostas Tsimikas - 5/10
Tsimikas's Liverpool career is just not getting the lift-off it needs, as he pulled up with yet another injury in this game.
Leighton Clarkson - 6/10
The youngster made his Liverpool debut and looked accomplished in the first half. His passing was superb, and he was snapping into tackles. In the second half, he became a lot more sloppy with his passing.
Naby Keita - 6/10
Keita nearly scored with a terrific strike from the edge of the box at the end of the first half. He really didn't get to his best in this game, but like Alexander-Arnold, these minutes were important after his comeback from a hamstring injury.
Takumi Minamino - 6/10
Minamino thought he had scored the winner in injury time, but his goal was disallowed after VAR deemed that the ball had struck Sadio Mane's arm in the buildup. He'd have hoped to have done better in the final third throughout the ga
Mohamed Salah - 7/10
Salah scored the goal that took him past Steven Gerrard as Liverpool's all-time top-scorer in the Champions League. It was a bit perplexing to see him play the whole of this dead rubber, though.
Diogo Jota - 5/10
Jota was wasteful on the counter-attack in this game, as his passing in the final third just didn't find its range. In addition, he also missed a great chance in the first half off a cross from Minamino.
Divock Origi - 4/10
Another game, another poor performance from Origi. The Kop cult hero's Liverpool career is hanging by a thread, and such performances don't do much to help his case.
Billy Koumetio - 5/10
Koumetio came on at half-time for his Liverpool debut. While he stood tall to win a few headers, he was also understandably a bit chaotic. He may have been better with a more senior partner than Rhys Williams alongside him.
Jordan Henderson - 6/10
The skipper once again made a difference with his long-range passing, and if not for VAR, would have played a critical role in another Liverpool winner.
Andy Robertson - 6/10
He would've hoped to have not played this game, but Tsimikas's injury meant that he had to come in for the last 30 minutes.
Roberto Firmino - 6/10
Firmino took up a deeper role in midfield but didn't get very involved, as Liverpool really didn't have much possession of the ball in the first half.
Sadio Mane - 6/10
He came on for the last five minutes and almost set up a winning goal but was deemed to have handled the ball.