An attacking Albion side with an on-form Bobby Zamora looked like winners from the off at Highfield Road. They just never actually managed to score.
The Seagulls did put one in the net on the half-hour, but Barrett's joy was short-lived as the linesman's flag denied him his moment of glory.
Things didn't go completely Albion's way - Coventry's Konjic came close to putting the home side ahead - but Coppell's team had the lion's share of the openings and half-chances.
Albion went into the match six points adrift of Stoke with two games in hand after a surprise 0-0 draw for their fellow strugglers at Leicester in a 1pm kick-off.
Coventry no longer have under-soil heating, but the pitch had been covered and was in pretty good condition considering there was snow in the West Midlands earlier this week.
Albion received an early warning about the influence of Coventry's player-manager McAllister.
In the second minute the 38-year-old midfielder's diagonal cross was headed over by new signing Sara.
Shaw showed why Coppell rates him so highly as a defender with an important clearance when Zamora tried to find Barrett inside the box with a low cross.
But Shaw was less sure a few minutes later. His poor clearance from Barrett's angled centre fell to Jones, whose angled drive flashed wide of the far post.
It would have been the perfect way for Jones to celebrate the 200th League appearance of his career as Albion continued to show plenty of enterprise in the opening stages.
Zamora turned away superbly from Konjic, the £2 million Bosnian defender wearing a mask to protect a facial injury.
It needed the combined force of two Coventry defenders to end Zamora's progress towards goal.
A mishit volley from close range by Zamora moments later was cleared by Konjic after Hyldgaard unconvincingly palmed away a Watson cross.
Partridge chipped over from outside the area, then Holdsworth ended a promising solo run with a shot from long range well wide of the target as Coventry tried to respond.
The Seagulls threatened again when Zamora tried to direct a far-post header from another Watson cross back across Hyldgaard.
It was clawed away by the Danish keeper but would not have counted in any case, as Zamora was narrowly offside.
Albion should have fallen behind against the run of play midway through the half.
The first corner of the contest, taken by McAllister, was not properly cleared and was headed back into the danger zone by Pead.
The ball fell to Konjic, who was unmarked six yards out. He had time to control it and virtually pick his spot but dragged his volley horribly wide of the far post.
It was a real defender's finish. The widely travelled Holdsworth, signed recently from Premiership strugglers Bolton, would surely have found the net in the same position.
Brooker, operating in a free role but mainly on the right, volleyed high and wide from the edge of the area from Konjic's uncomfortable clearance.
Zamora was causing Coventry all sorts of problems in the air and he was desperately unlucky not to give Albion a 27th minute lead.
The ball bounced once for him to strike a swivelling left-foot drive which rebounded off the upright, with Hyldgaard comprehensively beaten.
Jones, suddenly acting as an emergency central defender, did well to thwart Sara after Watson's free-kick from 20 yards hit the defensive wall and Coventry broke rapidly.
Albion thought they had taken the lead their enterprise deserved on the half-hour when Brooker touched on Watson's cross for Barrett to fire into the roof of the net.
The linesman, however, already had his flag raised as the Republic of Ireland International pulled the trigger and it was ruled out for offside.
If anything, Albion appeared to have benefited from the fortnight's break arising from the postponement against Wimbledon and at Norwich in the FA Cup last Saturday because of a power failure.
There was plenty of spark about their performance , although Cullip carried things a bit too far when he bundled into rival captain McAllister ten yards inside Albion territory.
McAllister was not best pleased, but Cullip received nothing worse than a lecture from referee Phil Crossley.
Coventry did not manage an effort on target until the 41st minute and even then it was a weak header at the far post by Sara from McAllister's corner straight into the arms of Kuipers.
Zamora jinked away from two Coventry players before firing straight at Hyldgaard from 20 yards approaching the break.
Albion had certainly enjoyed the better of the opening 45 minutes and could count themselves unlucky not to be in front.
The only concern for the Seagulls at the interval was that their superiority had not so far been reflected in the scoreline.
More was expected of Coventry in the second half, which Partridge launched with a positive run brought to an end by a firm tackle by Cullip.
At the other end Hyldgaard did well to hold a low 30-yarder from Pethick, with Albion players ready to pounce.
Mayo came to the Seagulls' rescue twice in a matter of minutes, first with a fine challenge on Sara inside the area which had Coventry fans appealing optimistically for a penalty.
Mayo then cleared Partridge's cross from a quickly taken free-kick by McAllister which caught the Albion defence napping.
In-between, Sidwell headed wide of the far post from a Watson cross. It was by no means a straightforward chance, but Sidwell has been in such goalscoring form that he held his head in his hands.
Cullip was the next to come close, heading narrowly over when Coventry failed to deal with a Watson corner.
Albion had penalty appeals of their own rejected as Sidwell went down under a challenge by Betts from Watson's cross.
Watson, having his most influential match for some time, fed Zamora for a right-foot shot which went wide of both the far post and the lunging Sidwell.
The only surprise, given the number of openings and half chances they had created, was that Albion had not yet managed to score.
Coventry made a change upfront, McSheffrey coming on for the ineffective Sara.
There was no evidence of the 16 places and 23 points dividing the sides at the start of play as Albion continued to look the likelier winners.
Coventry made a second substitution, introducing striker Mills for midfielder Eustace, and they almost grabbed an undeserved lead immediately afterwards.
McAllister got the better of challenges from Mayo and Jones to release Partridge for a fierce shot which forced the rarely troubled Kuipers into a flying stop at the expense of a corner.
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