City slipped to a narrow defeat to Luton Town in Championship action at the Coventry Building Society Arena.
Elijah Adebayo scored the only goal of the game midway through the first half, in what proved to be the winner.
The Sky Blues started immediately on the front foot and the first chance came after 12 seconds when a ball down the right was played through for Matty Godden, but his shot was well saved by Palmer.
City continued to push early on, and it was Matty’s strike partner Viktor Gyokeres who had the next chance two minutes later, but he couldn’t convert Gustavo Hamer’s through ball, as he sent his shot wide.
At the other end, the Hatters first opportunity of the game came to Luke Berry and the midfielder tried his luck from range, but his shot was straight at Simon Moore.
Hamer was continuing to cause the Luton defence problems, this time he won the ball back in midfield and charged forward, sliding the ball in for Viktor, but he was denied by Palmer in the Luton goal.
However, despite City’s good work in the early moments of the game it was the visitors who took the lead and it was Elijah Adebayo who scored from a tight angle to make it 1-0.
HALF-TIME: Sky Blues 0-1 Luton Town
The Sky Blues started the second half the brightest and they had their first chance of the second 45 through Kyle McFadzean, but his header only landed on top of the netting.
Ian Maatsen was the next City player to go close as he cut inside onto his right foot and looked for goal, but his shot went inches over the bar.
Simon Moore was called into action for the first time in the second half as he had to be alert to deny Adebayo from close range and then on the follow-up, Kyle McFadzean blocked Tom Lockyer’s effort.
City continued to push for an equaliser at the other end and had a flurry of chances, first Viktor Gyokeres saw his shot deflected behind for a corner and from the resulting set-piece, Hamer’s corner hit the top of the netting.
Mark Robins introduced Fabio Tavares with ten minutes to go and he almost made an immediate impact when he ran towards goal and picked out Callum O’Hare, but his shot was saved by Palmer.
City had one more chance deep into stoppage time, but Todd Kane's cross into the box was headed into the side-netting by Ian Maatsen.
FULL-TIME: Sky Blues 0-1 Luton Town
Attendance: 16,996 (1,757 away)
Referee: Oliver Langford
Yellows: Amari’i Bell, Jamie Allen, Jake Clarke-Salter, Harry Cornick, Cameron Jerome, Elijah Adebayo, Reece Burke, Kyle McFadzean
Goalscorers: Elijah Adebayo
Sky Blues XI: Simon Moore (GK), Todd Kane, Kyle McFadzean©, Michael Rose, Jake Clarke-Salter, Ian Maatsen, Gustavo Hamer, Jamie Allen, Martyn Waghorn (63’ O’Hare), Matty Godden (80’ Tavares), Viktor Gyokeres.
Unused Subs: Ben Wilson (GK), Josh Reid, Ben Sheaf, Ryan Howley, Ricardo Dinanga.
Luton Town XI: Alex Palmer (GK), James Bree, Dan Potts, Tom Lockyer (85’ Lansbury), Reece Burke, Amari’i Bell, Jordan Clark, Luke Berry (72’ Campbell), Pelly Ruddock Mpanzu, Harry Cornick (59’ Jerome), Elijah Adebayo.
Unusued Subs: Harry Isted (GK), Robert Snodgrass, Carlos Mendes Gomes, Admiral Muskwe.