The Sky Blues endured a frustrating evening as nine-man Scunthorpe held on for a point at the Ricoh Arena.
Skipper Michael Doyle put the home side ahead from the penalty spot in the 51st minute after Iron goalkeeper Joe Murphy was sent-off for bringing down Jay Tabb in the area.
But Scunthorpe levelled when Jack Cork converted a Marcus Williams cross and despite a late red card to defender Kelly Youga, City failed to find the elusive winner.
City boss Iain Dowie made three changes to the side beaten at Norwich four days earlier.
Leon McKenzie replaced the injured Kevin Kyle in attack while Isaac Osbourne made way for Julian Gray as Dowie reverted to a conventional 4-4-2 formation.
Arjan De Zeeuw was rested for the clash, so Elliott Ward also returned at the heart of the defence.
McKenzie fired straight at Murphy before the 'keeper did well to hold an acrobatic over-head-kick from Marcus Hall as the Sky Blues began brightly.
A great sliding challenge from Ben Turner then denied Paul Hayes after skilful play from Jonathan Forte created an opening for the visitors before Doyle shaved the post with a shot from the edge of the area.
City thought they been awarded a penalty in the 29th minute when referee Mick Jones pointed to the spot after Youga sent Jay Tabb tumbling.
However, after consulting his linesman, Jones ruled the offence had been committed outside the box and David McNamee fired the resultant free-kick narrowly wide of the far post.
But Jones was in no doubt when he again pointed to the spot in City's favour three minutes after the break.
McKenzie sent Tabb through on goal and Murphy sent the midfielder sprawling as he looked to go round the stranded 'keeper.
Jones immediately reached for his top pocket and showed Murphy an inevitable red card.
Doyle stepped-up to take the penalty and sent Scunthorpe substitute Josh Lillis the wrong way for his third goal of the campaign.
The home side's lead was almost short-lived, though, as Jim Goodwin's superb free-kick cannoned back off the underside of the crossbar with Konstantopoulos beaten.
Gray then skewed wide of the target after good link-up play between Doyle and Tabb found the winger in the area before Dele Adebola shot tamely at Lillis.
But the visitors did find an equaliser in the 68th minute when Williams crossed from the left and on-loan Chelsea man Cork, son of former City assistant boss Alan, stabbed home from close-range.
Boss Dowie introduced substitutes Ellery Cairo, Wayne Andrews and Michael Hughes in hope of freshening up the Sky Blues attack.
And the move almost paid dividends with 12 minutes left when Andrews failed to make a firm connection Cairo's teasing cross from the left before Scunthorpe were reduced to nine-men when Youga was dismissed for two bookings in quick succession.
That made for a tense finish, but despite heavy late pressure City failed to take capitalise on their numerical advantage as Andrews, Hall and Adebola all squandered late chances to score.
Coventry City: Konstantopoulos, McNamee, Ward, Turner, Hall, Tabb (Cairo, 71), S Hughes (M Hughes, 79), Doyle (c), Gray, McKenzie (Andrews, 75), Adebola. Subs (Not Used): Osbourne, Borrowdale.
Goals: Doyle (51 pen)
Booked: M Hughes
Scunthorpe Utd: Murphy, Youga, Crosby (c), Butler, Williams, Logan (Taylor, 46), Goodwin (Paterson, 90), Cork, Hurst (Lillis, 49), Forte, Hayes. Subs (Not Used): Baraclough, Ameobi.
Goals: Cork (68)
Booked: Youga, Lillis
Sent-off: Murphy (50), Youga (84)
Attendance: 14,036 (636 Scunthorpe)


















