But Sunday’s beaten FA Cup semi-finalists had largely themselves to blame as their own hopes of a second trip to Wembley in successive months were ended by three soft goals.
The Sky Blues gifted Jaden Philogene’s first-half opener, as well as Hull substitute Noah Ohio’s 78th-minute winner with his first touch – while they were also on the wrong end of a contentious penalty.
Twice the Sky Blues levelled, first through Kasey Palmer’s superb free-kick and then Bobby Thomas’s header but Thomas’s under-hit backpass allowed Ohio to hit the winner just two minutes after leaving the bench to lift the Tigers back to within three points of sixth-placed Norwich City.
And that leaves Coventry nine points adrift with three games left, a worse goal difference than Norwich – and needing snookers.
After Sunday’s heart-breaking drama for the Sky Blues at Wembley, this game always threatened to be a real mental challenge for the hosts.
It took over half an hour for the game to come to life when keeper Collins made a mess dealing with Philogene’s far from fiercely struck low right-foot shot – and allowed it to squirm under his body for Hull’s 31st-minute opener.
Palmer took just five minutes to level when he curled home a stunning right-foot free-kick into the top left corner. But, on the stroke of half-time, Hull were back in front.
Joel Latibeaudiere was adjudged to have brought down Liam Delap, but video replays showed that the moment of contact appeared to come just outside the penalty area.
Carvalho was completely unnerved as he duly despatched a coolly-taken right-foot penalty. But the Hull celebrations lit the sky blue touch paper- and it led to a mass altercation between 21 of the 22 players, which brought four bookings.
City boss Mark Robins at least had the option of throwing on both his two big goal-scoring targetmen Haji Wright and Ellis Simms into the fray at half-time. And, on 58 minutes, the hosts were level when Thomas got his head Jay Dasilva’s cross to scramble home a second equaliser.