The Sky Blues have been beaten at the Globe Arena after goals from Vadaine Oliver and Callum Lang.
Oliver gave Morecambe the lead late on in the second half by flicking the ball home from a set-piece.
Mark Robins' side grew into the game slowly, but it was the home side who doubled their lead midway through the second half through Lang, with his first touch of the game.
The Shrimps came close to opening the scoring inside seven minutes. Vadaine Oliver came together with Lee Burge leaving Garry Thompson with a clear shot at goal but Rod McDonald, back in the eleven after missing last week's win over Boreham Wood with concusion, was on hand to nod the ball off the line.
In fact, Thompson was unlucky not to be on the scoresheet a number on times throughout the first half. Moments later, the number seven saw his header tipped over from close range by Burge.
City were growing into the game, but it was Morecambe's Lewis McGurk who rattled the woodwork midway through half. The former Portsmouth midfielder wriggled inside before unleashing a thunderbolt from 35-yards, beating Burge but not the far post.
The Shrimps' opener was coming. Oliver came close again racing onto a direct throughball before being denied again by Burge before finally latching onto a set-piece to prod home and give Jim Bentley's side a deserved lead.
The Sky Blues started the second half simular the first. Peter Vincenti and Devon Kelly-Evans came on but neither made an impact as big as Morecame substitute Callum Lang. The 19-year-old, on loan from Wigan, skillfull shifted the ball onto his left with his first touch of the afternoon and fired home with his second to double the Shrimps' lead.
Marc McNulty came close to pulling Mark Robins' side back into the game. The striker turned well in the area before beating Shrimps 'keeper Barry Roache and clattering the post. It was not going to the the Sky Blues' day.
Yellows: McGurk (10')
Goals: Oliver (36'), Lang (66'), Rose (82').
Coventry City XI: Burge (GK); Grimmer, Willis, McDonald, Haynes; Stevenson, Doyle (C); Nazon (Vincenti 45'), McNulty, Shipley (Dev. Kelkly-Evans 45'); Biamou (Beavon 76').
Subs: O’Brien (GK), Stokes, Bayliss, Davies.
Morecambe XI: Roche (GK), McGowan, Muller, Old, Brough, Thompson, Fleming, Oliver, Osborne (Lang 66', Conlan 89'), Rose (C), McGurk (Campbell 66').
Subs: Nizic (GK), Lund, Kenyon, Hedley.