City were forced to settle for a point against Luton Town at the Coventry Building Society Arena.
The Sky Blues had fallen behind after 40 seconds when Tom Lockyer opened the scoring, but City responded just before the break-through Matty Godden.
City were reduced to ten-men with five minutes on the clock, as Josh Wilson-Esbrand was shown a second yellow.
The visitors made the perfect start to the game, taking the lead within the first 40 seconds, after a ball into the box was deflected off Kasey Palmer into the path of Tom Lockyer, who tapped in from close range.
City looked to make an immediate response and they almost did that when Viktor Gyökeres beat his man and fired an effort at goal from the edge of the area, but it was saved well by Ethan Horvarth.
The resulting corner was put into the box by Josh Wilson-Esbrand on his first start, and it fell towards the path of the returning Kyle McFadzean, but his shot went wide of goal.
At the other end, Alfie Doughty whipped in a corner which was met by the head of Elijah Adebayo, but it was a comfortable stop for Ben Wilson.
Wilson had to be alert with another Doughty corner, as the in-swing was palmed over the bar by the City ‘keeper.
Then, just before the break, an excellent ball from Callum Doyle released Matty Godden and he pulled the ball back across goal for Gyökeres, but he was pulled to the ground by Gabe Osho and the referee pointed to the spot.
Godden was the man to step-up, and he made no mistake, sending his penalty down the middle and beating Horvath to draw the game level heading into half-time.
HALF-TIME: Sky Blues 1-1 Luton Town
After the restart, it was the Sky Blues who went closest to taking the lead and it came through an unlikely source, as Luke McNally went on a run and forced Horvath into a save with a shot from the edge of the area.
Kyle McFadzean was doing Kyle McFadzean things five minutes later, stopping a two-on-one attack from the visitors, coming out on top with a superb challenge.
City thought they had their second of the game on the hour-mark when Kasey Palmer produced a moment of magic, but his curling effort came back off the crossbar.
Luton introduced Cauley Woodrow and forced Ben Wilson into a stunning save from close range, with the ‘keeper at full stretch to deny the striker.
City were reduced to ten men with five minutes left on the clock, after Wilson-Esbrand was shown a second yellow card.
FULL-TIME: Sky Blues 1-1 Luton Town
Yellows: Reece Burke, Gabe Osho, Amari’I Bell, Josh Wilson-Esbrand, Carlton Morris, Kyle McFadzean
Reds: Josh Wilson-Esbrand
Goals: Tom Lockyer; Matty Godden
Attendance: 20,366 (2,843 visiting supporters)
Sky Blues XI: Ben Wilson (GK); Luke McNally, Kyle McFadzean (C), Callum Doyle, Josh Eccles (69’ Norton-Cuffy), Gustavo Hamer, Jamie Allen (90' Bidwell), Kasey Palmer, Josh Wilson-Esbrand, Viktor Gyökeres, Matty Godden (81’ Walker).
Subs: Simon Moore (GK); Jake Bidwell, Michael Rose, Brooke Norton-Cuffy, Jack Burroughs, Sean Maguire, Tyler Walker.
Luton Town XI: Ethan Horvarth (GK); Tom Lockyer (C), Carlton Morris, Elijah Adebayo (69’ Woodrow), Marvelous Nakamba, Reece Burke, Pelly Mpanzu, Jordan Clark (87’ Taylor), Amari'i Bell, Gabe Osho, Alfie Doughty (65’ Onyedima).
Subs: James Shea (GK); Luke Berry, Cauley Woodrow, Henri Lansbury, Allan Campbell, Fred Onyedima, Joe Taylor.