Sky Blues still searching for first win after difficult night at the Greenhous Meadow Stadium
Coventry City slipped to a fourth league defeat at Greenhous Meadow after a double from Matt Richards and strikes from Darren Jones and Marvin Morgan for Shrewsbury.
Darren Jones headed the home side infront after just two minutes with Matt Richards' fortunate deflection doubling the Shrews' advantage 18 minutes later.
Richards then stepped up to convert a penalty he won just after the hour with Morgan making it four-nil just moments later and City substitute John Fleck converting a consolation penalty with 16 minutes to go.
Caretaker City boss Richard Shaw made no changes to the side that suffered a late defeat to Tranmere Rovers at the weekend, sticking with an unchanged line-up for the clash at the Greenhous Meadow Stadium
It was not the best of starts for the Sky Blues though as former City defender Jermaine Gradison tussled with Carl Baker and Steven Jennings to win a corner.
The resulting deep delivery from Paul Parry found Jones at the back post who beat Joe Murphy to the ball to head a looping header home and give the hosts the lead after just two minutes.
It could have been two on nine minutes when William Edjenguele held back Marvin Morgan to earn himself a booking, the resulting free kick delivery seeing a wayward clearing punch from Murphy almost find its way into the net only to be cleared off the line by the head of Richard Wood.
It was two after 20 minutes though thanks to a bit of bad fortune for the Sky Blues.
Edjenguele gave a free kick away after another tussle with Morgan and Parry then stepped up to fire in a dead ball effort which deflected off Richards and gave Murphy no chance as it flew into the net.
The Sky Blues started to get a foothold in to the game midway through the half with David McGoldrick and Stephen Elliott trying to stretch the Shrewsbury back four with some bending runs and hold up play.
It was the home side who went closest to the next goal though when, after 39 minutes, Morgan played a neat one-two with Terry Gornell who took one touch too many and poked his finish under the rushing Murphy but guided it just wide of the far post.
Richard Shaw responded to the first half showing by making two half time changes, bring John Fleck and Billy Daniels on for Adam Barton and Carl Baker.
The switch seemed to have the desired effect early on as the Sky Blues spent the first five minutes of the second half camped out in Shrewsbury's half.
Completely against the run of play the hosts thought they had a third though after 53 minutes when Parry's low drive from just under 25 yards took a deflection off Gornell, wrong-footed Murphy and trickled into the net.
This time fortune was with City though as the linesmans flagged Gornell for offside.
Town made it 3-0 just after the hour though when Richards fell in the area under a challenge from Edjenguele before dusting himself off to convert the spot kick.
No sooner had Shrewsbury made it three they then grabbed a fourth through Morgan who dispossessed Wood after a high ball downfield and fired past Murphy.
The Sky Blues nearly got on back on 67 minutes when Fleck's cross on the by-line found Elliott whose close range header was kept out by some lightning reflexes by Shtrewsbury 'keeper Chris Weale.
Grandison was then required to make a goal saving block with 20 minutes to go to deny McGoldrick's effort from a tight angle just inside the area.
McGoldrick had another chance after 72 minutes when he outmuscled Grandison to go one-on-one with Weale only to poke his finish just wide.
City did get one back with 16 minutes to go when Gary McSheffrey was bundled over in the area by Grandison, leaving fellow sub Fleck to open his competitive account for the club by driving a no-nonsense spot kick straight down the middle.
McSheffrey nearly got a second back for City deep into injury time with a 20-yard half volley which was tipped over the bar by Weale.
But that was the last effort for the Sky Blues on a difficult and disappointing night which left them still searching for their first win in League one.
Attendance: 5,960 (610 Sky Blue Army)
CoventryCity: Murphy, Clarke, Hussey, Wood, Edjenguele, Barton (Fleck 45), Kilbane (c) (McSheffrey 63), Baker (Daniels 45), Jennings, Elliott, McGoldrick
Subs: Dunn (GK), McDonald, O'Donovan, Brown
ShrewsburyTown: Weale, Grandison, Jacobson, Summerfield, Jones, Richards (c) (Wright 71), Morgan, Parry, Wildig, Hector, Gornell (Taylor 82)
Subs: Anyon (GK), Purdie, Wright, Hall, Doble, Goldson
Bookings: Edjenguele (COV), Wood (COV)