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Gillingham are now four games without a win at the start of their League 1 campaign.
Dom Hyam deservedly put Coventry ahead after dominating the opening half of Saturday’s clash.
The Gills were much brighter after the turnaround at St Andrew’s - Coventry’s temporary home in Birmingham - but were unable to make it count.
There was just one change for the Gills, with Regan Charles-Cook (hamstring) returning to the side and replacing Elliott List in the starting XI.
But his afternoon was cut-short as manager Steve Evans made a tactical change with half an hour gone. By then the Gills were a goal behind and it could have been more.
Gills keeper Jack Bonham had to make a good early save to deny Matty Godden, who had met Wesley Jobello’s deep cross, and Max Ehmer did enough to prevent the striker from tucking away the loose ball.
Jobello went close himself with a header from Jordan Shipley’s free-kick and the Gills remained largely on the backfoot until conceding in the 26th minute.
Mark Byrne’s block from Zain Westbrooke had led to a corner and when the same Coventry player whipped in the flag-kick, Hyam was there to pounce after Bonham came out and missed the cross.
Godden had another chance off the line while Evans prepared to make a change. The Gills went from a diamond formation to four across the middle and Charles-Cook was the man withdrawn.
Just before the switch the Gills had their best chance of the opening 45 minutes. A delightful ball forward from Stuart O’Keefe sent Alex Jakubiak away on goal, with two defenders for company. He did well to get a shot away at goal but keeper Marko Marosi was equal to it.
Coventry’s chances dried up in the last 15 minutes, as the Gills got to grips with their passing and movement. A stoppage-time opportunity for Mikael Ndjoli was lashed wide.
There were half chances early in the second half for the Gills, as Alfie Jones won good possession but Hanlan’s resulting cross was cleared and nothing came of a corner either, moments later.
Ehmer and Connor Ogilvie needed to be in the right place at the right time to prevent the hosts from adding an early second, before Godden flashed a header wide from Sam McCallum’s great delivery.
Ndjoli fired wide for the improving Gills, who began playing with more confidence, although clear-cut chances were hard to find. Hanlan headed a corner wide with half an hour left.
Substitute Ndjoli had put a couple of shots wide from normal play but came close to an equaliser with a free-kick that had power and precision, only for Marosi to get across well for a diving save, just as the ball looked to be heading for the top corner.
Ogilvie’s header from a free-kick was beaten away by Marosi who finished the game with a clean sheet.
Gillingham: Bonham, Hodson, Fuller, Ehmer, Ogilvie, O’Keefe (List 63mins), Jones, Charles-Cook (Ndjoli 31mins), Byrne, Jakubiak, Hanlan (Mandron 85mins). Subs not used: Walsh, Cisse, Marshall, Woods.
Coventry: Marosi, Mason, Hyam, Rose, Kelly, Westbrooke (O’Hare 67mins), Shipley, McCallum, Godden (Bakayoko 80mins), Jobello (Wakefield 80mins), Hiwula. Subs not used: Wilson, Williams, Eccles, Bapaga.
Attendance: 5,624 (383 away)