They made hard of work of it, continuing the pattern of their season so far. Somewhere they have lost the extra ingredient that enabled them to turn good performances into winning ones last season, sparing them the familiar struggle to avoid relegation. Unless they can string together victories, the bad old days are liable to return.
They usually held the upper hand against a Wednesday side who looked woefully short of confidence and yet laboured to turn their superiority into tangible advantage, even with McAllister bringing class and authority back to their midfield.
The Scotland captain had been missing for 10 months with a knee ligament injury that required surgery last summer and denied him the honour of leading his country into the World Cup finals. At almost 34 he can ill afford more setbacks yet showed no lack of commitment here. Indeed, he almost marked his comeback with a goal when a drive from almost 40 yards was punched away by Wednesday's Kevin Pressman, who had by far the busier afternoon of the two goalkeepers.
Until Dublin, whose goal was only his third of the season, struck the woodwork early in the second half, McAllister's effort had been as close as the home side had been to a goal, although Pressman did deny Whelan at his near post.
The Yorkshire-born forward, who started the match alongside Dublin in the middle but moved to the right when Darren Huckerby entered the fray in the second half, was at the heart of most of Coventry's better moves, whether running at the Wednesday defence or setting up chances for others.
It was a performance that did nothing to resolve the dilemma of their manager, Gordon Strachan, over what is Whelan's best position, since in neither position was he more or less effective than the other. What is clear is that his well-being has benefited from the ending of police inquiries into an incident in Nottingham earlier in the season when officers were called to a disturbance at a party he was attending.
Unsurprisingly, it was from his pass that Dublin at last ended Coventry's frustrations with just over a quarter of an hour remaining. Whelan drilled in a low cross to the near post and Dublin, given too much space, flashed the ball beyond Pressman's reach.
Wednesday, though still a point better off than Strachan's charges, look to have the more worrying future. Danny Sonner, signed from Ipswich last week, made a good impression on his debut but the influence of the Dutchman Wim Jonk is still peripheral and the Italian, Benito Carbone, seemed lost without his partner, Paolo di Canio, whose fate Wednesday still await after the incident with referee Paul Alcock that resulted in his suspension by the club.
Goals: Dublin (74) 1-0.
Coventry City (4-4-2): Hedman; Nilsson, Breen, Shaw, Edworthy; Telfer (Huckerby 64), McAllister, Boateng, Froggatt; Whelan, Dublin. Substitutes not used: Williams, Soltvedt, P Hall, Ogrizovic (gk).
Sheffield Wednesday (4-4-2): Pressman; Atherton, Thome, Walker, Briscoe; Alexandersson, Sonner, Jonk, Humphries; Booth, Carbone (Whittingham 83). Substitutes not used: Newsome, Magilton, McKeever, Clarke (gk).
Referee: D Elleray (Harrow).
Bookings: Coventry: Telfer.
Man of the match: Whelan.
Attendance: 16,006.Reuse content