Pep Guardiola’s side missed a chance to book their place in the last 16 after VAR controversially disallowed Rodri’s goal and, less debatably, dismissed Gomez for a professional foul.
Mahrez’s latest spot-kick misfire came in the first half prior to Gomez’s premature exit.
And with Erling Haaland rested on the bench ahead of City’s trip to Liverpool on Sunday, the Premier League champions failed to score for the first time in 24 games in all competitions.
They would have been guaranteed to progress from Group G with a win, but instead had to be satisfied with avoiding defeat after playing with 10 men for an hour.
City are still on course to qualify for the last 16 after taking 10 points from their first four games, but they will have to wait until Borussia Dortmund’s game against Sevilla later on Tuesday to determine if they are through with two games to spare.
It was notable that City lacked a cutting edge without Haaland, who has scored an incredible 20 goals in 12 competitive games since signing from Dortmund in the close-season.
Haaland scored twice in just 45 minutes during last week’s 5-0 drubbing of Copenhagen, but Guardiola might have expected his team to dominate the Danish minnows even without him.
But Copenhagen had only lost one of their previous 13 Champions League home group games and, aided by the VAR mayhem, they proved tougher opponents at the Parken Stadium than they had in Manchester.
– Mahrez misery –
Julian Alvarez was picked to deputise for Haaland and the young Argentine wriggled into the Copenhagen area for a low strike that flashed just wide in the opening minutes.
Rodri thought he had given City the lead with a 25-yard rocket in the 11th minute.
But after a lengthy VAR check, the midfielder’s goal was harshly disallowed for handball by Mahrez in the build-up, even though the Algerian had no control over the ball’s accidental contact with his arm.
Ederson had to tip over Lukas Lerager’s drive from just outside the area after City’s defence were caught out of position moments later.
After being denied by VAR, City should have benefitted from the system in the 24th minute, winning a penalty after a replay check of Nicolai Boilesen’s handball when he blocked Manuel Akanji’s header.
However, not for the first time in a City shirt, Mahrez was unable to convert the spot-kick as Kamil Grabara dived to his right to make a fine save.
Remarkably, VAR would intervene yet again after half an hour when City left-back Gomez was caught the wrong side of Hakon Haraldsson and hauled down the Copenhagen midfielder.
After play had continued for several seconds without a foul being given, referee Artur Dias went to the pitchside monitor and returned to show Gomez the red card.
City were the first team to miss a penalty and have a player sent off in the first half of a Champions League game since Arsenal against Bayern Munich in 2014.
Trying to overcome City’s numerical disadvantage, Kevin De Bruyne’s curler from the edge of the area forced a good save from Grabara early in the second half.
But City found it hard to establish their usual stranglehold on possession and had to settle for a point after Joao Cancelo’s late drive was saved by Grabara.
