Dele Adebola's 85th minute shot from 12 yards earned Coventry three barely-deserved points after they were largely outplayed by the home side.
With no more than pride to play for, Stoke had the better of the early stages, with Dave Brammer, Michael Duberry and Adam Rooney going close.
But as the game wore on, Stoke's lack of success seemed to frustrate them.
And with five minutes left, the impressive Kevin Thornton set up Adebola to fire home the winner.
Stoke manager Johan Boskamp on his future:
"The chairman has asked me to wait until Friday for a definite decision but I've waited long enough.
"I've turned down offers from two clubs already and I will talk to the next team who are interested.
"I'd be disappointed to leave because I want to stay. As things stand I will be going back to Belgium on 2 May."
Coventry manager Micky Adams:
"Our play was a bit predictable until we put Dele Adebola on. He gave us something different.
"All of the lads did their jobs but I was especially pleased with our defenders who fought for everything.
"We finally seem to have found a winning formula although it has come too late for this season."
Stoke: Simonsen, Hoefkens, Duberry, Hill, Dickinson, Paterson (Hazley 68), Russell, Brammer (Henry 45), Gallagher, Sidibe, Rooney.
Subs Not Used: de Goey, Kopteff, Broomes.
Coventry: Fulop, Whing, Heath, Hall, Giddings, Thornton, Hughes, Doyle, McSheffrey (Morrell 80), Hutchison (Adebola 64), John (Turner 89).
Subs Not Used: Osbourne, Williams.
Goals: Adebola 85.
Ref: P Walton (Northamptonshire).