A hat-trick from Vincent Pericard condemned the Sky Blues to a 3-1 defeat at Home Park against Plymouth Argyle this afternoon.
The on-loan Portsmouth striker hit home twice before the break and once to send City to their second successive away defeat.
Substitute Dennis Wise netted a consolation for City - his fifth goal for Coventry.
Micky Adams made three changes to the side which beat Sheffield Wednesday 2-1 on Wednesday night.
Don Hutchison came into the centre of midfield for Dennis Wise, who was rested, while James Scowcroft returned from suspension and replaced Andy Morrell on the left hand side of midfield with McSheffrey moving to the right.
Andy Impey started at right-back after recovering from a groin strain, meaning Matt Heath moved into the centre-back position in the absence of Robert Page, who was suspended. Michael Doyle captained the side.
For Plymouth, Lilian Nalis made an appearance against the Sky Blues, who he spent a spell on loan with earlier in the campaign.
Coventry pressed early and got a corner in the second minute - Scowcroft flicking on for Adebola, who forced the Pilgrims to clear behind. But it came to nothing as Hutchison saw his set-piece cleared.
And despite some good possession from the Sky Blues, it was the home side who boasted the next opportunity with 11 minutes on the clock. McSheffrey was caught in possession by Tony Capaldi on the left flank and the ball found its way to Nalis, who produced a good cross which David Norris headed wide of the upright.
The Sky Blues found themselves behind on 13 minutes through Pericard, who was making his first full start at Home Park. From an Argyle corner, the Cameroon international made no mistake as he fired a right-footed shot past Fulop in the City goal.
Argyle could have had another on 17 minutes - again from a penalty area melee. Nalis originally say his shot blocked before the ball came out to Wotton, who forced Fulop to turn his effort wide.
On 28 minutes, the Sky Blues threatened in close succession. Firstly, McSheffrey played a neat one-two with Whing before forcing Larrieu to parry away at his near post before a minute later, Doyle's shot from distance rose inches over the crossbar.
Evans forced a save from Fulop with his head on 35 minutes, before at the other end, Stern John rolled a low shot at Larrieu, to no avail.
And it was disaster for the Sky Blues on 42 minutes, when Pericard stroked the ball home to double the deficit, though the City defence argued he was in an offside position.
McSheffrey forced the City stopper into a flying save as the visitors attempted to claw something back, while Larrieu also had to be alert to save Elllott Ward from what would have been an embarrassing own-goal moments later.
Plymouth emerged as the brighter side after the interval and boasted the first opportunity, albeit with a helping hand from the Sky Blues. Impey accidentally played the ball into the path of Pericard, who in turn found Micky Evans in the box - the latter forcing an excellent block save from Heath.
Scowcroft shot wide for the visitors on the hour before Argyle made the first change of the game moments later, when Chadwick replaced Evans.
Argyle created another chance with 65 on the clock when Capaldi's cross found Norris, who forced Fulop to save, while at the other end, John forced Larrieu to palm his shot over the crossbar from the edge of the D.
City were beginning to see more of the ball and on 68 minutes, Adebola forced a corner from Larrieu, who had to turn the ball away at his near post.
But the scoreline took a turn for the worse in the 74th minute, when Pericard completed his hat-trick. A mix-up in the defence between Fulop and Heath saw the striker through clean on goal from a Capaldi through-ball and he made no mistake as he trundled towards the goal before whacking it in from close range.
Adams made a triple substitution in the 78th minute, with Wise, Claus Jorgensen and Andy Morrell replacing Doyle, Scowcroft and Adebola. Wise made an immediate impression as he was booked 40 seconds after arriving on the pitch.
But his effort was more productive in the 83rd minute when the veteran midfielder pulled back a goal for the Sky Blues and linking up with Jorgensen's pull back.
But with defeat on the horizon, McSheffrey deepened the wound by getting booked in the 90th minute - his 10th yellow card of the season, meaning he will now serve a two-match ban.
Plymouth: Larrieu; Nalis; Norris (Buzsaky, 82); Evans (Chadwick, 60); Pericard; Kouo-Doumbe; Capaldi; Wotton; Aljofree (Djordic, 82); Ward; Connolly.
Subs: Hodges; McCormick;
Coventry: Fulop; Whing; Williams; Doyle (Wise, 78); Adebola (Morrell, 78); McSheffrey; Scowcroft (Jorgensen, 78); John; Heath; Hutchison; Impey.
Subs: Ince; Thornton.
Referee: Paul Armstrong
Bookings: Williams (42); Wise (79); McSheffrey (90)
Attendance: 12,958 (741 City fans)
