Manchester were held in a 0-0 stalemate with FC Copenhagen on Tuesday.
So Manchester City dropped their first Champions League points of the season.
Sergio Gómez was made to play with 10 men in 30 minutes after showing the red card.
As a result, the Premier League champions struggled to dominate their opposition and failed to score this season.
On Tuesday Borussia Dortmund's 1-1 draw Secured City's place in the 16-round with Sevilla.
City coach Pep Guardiola said, "Many players didn't start today because they were tired and tired and swallowed"
After striking 25 yards Past Kamil Grabara the Spanish midfielder gave City the lead in 11 minutes.
The ball hit Mahrez's hand lightly when he was fighting between the defenders for an aerial ball.