The Sky Blues slipped into the bottom half of the table as Sheffield United edged a closely contested clash at the Ricoh Arena.
A 61st minute header from Chris Armstrong was enough to give Bryan Robson's Blades victory and stretch City's winless streak in the Championship to four matches in the Championship.
Iain Dowie's men battled hard in search of an equaliser but struggled to break through the visitors' stubborn resistance.
Their best chances arrived in the first-half where Ellery Cairo, skipper Michael Doyle and Dele Adebola all failed to find a way past Paddy Kenny.
Dowie was forced into a last minute change ahead of the game full-back Marcus Hall missed out with an Achilles injury and Gary Borrowdale stepped-in for his first appearance since suffering an ankle injury in October.
Arjan De Zeeuw also returned at the back while winger Cairo made his sixth start of the season in place of Leon McKenzie after impressing as a late substitute against Scunthorpe in midweek.
The visitors boasted the Championship's top scorer in James Beattie upfront - and the former England striker had the first effort on goal when his header was deflected wide by City full-back David McNamee
Michael Tonge then found Chris Armstrong in the area but Dimi Konstantopoulos was equal to the midfielder's scuffed shot, parrying the ball behind for a corner.
A left-footed drive from Cairo flashed wide of the target at the other end, before a moment of quality from the Dutchman almost produced the opening goal on the half-hour mark.

Cairo latched onto the ball with his back to goal on the edge of the area and unleashed a fierce volley which Blades 'keeper Kenny did brilliantly to the push the ball over the bar at full-stretch.
Konstantopoulos was then on hand to keep out strikes from Tonge and Beattie before Kenny clawed away a goal-bound effort from Doyle at the back-post.
A slip from the visitors' on loan Aston Villa defender Gary Cahill presented the Sky Blues with a glorious chance to score in first-half stoppage-time, but Adebola skewed wide with only Kenny to beat.
A glancing header from Beattie was tipped over by Konstantopoulos just after the break before the dangerous frontman turned provider as the Blades went ahead on the hour.
Beattie darted past Borrowdale on the right and crossed to the back-post where Armstrong ghosted in to head the ball into the far corner via a deflection off Arjan De Zeeuw.
Doyle fired wide from 25-yards as the Sky Blues looked for an immediate response but United were standing firm at the back and could have even doubled their lead with eighteen minutes left but Keith Gillespie blasted into the side-netting.
The Sky Blues continued to throw men forward in search of an equaliser but substitute Wayne Andrews fired their best chance high and wide from an acute angle late on.
Coventry City: Konstantopoulos, McNamee (Osbourne, 46), De Zeeuw, Turner, Borrowdale (Andrews, 80), Cairo (McKenzie, 65), Tabb, S Hughes, Doyle (c), Gray, Adebola. Subs (Not Used): Marshall (GK), Ward.
Goals: None
Booked: Adebola, Borrowdale
Sheff Utd: Kenny, Bardsley, Cahill, Kilgallon, Naysmith (c), Gilliespie, Tonge, Montgomery, Armstrong, Carney (Webber, 84), Beattie. Subs (Not Used): Gerrard (GK), Bromby, Stead, S Quinn.
Goals: Armstrong (61)
Booked: Bardsley
Attendance: 20,355 (2488 Sheff Utd)


















