But while Chris Coleman's side are three points outside the top six and remain in a battle, Gannon wrote off Posh's chances of playing in the second tier next season as they were left 13 points adrift of safety, having won just five games all season.
He said: "We have to put ourselves out of our misery and accept that we are going down.
"We would need to get three times as many wins as the club has managed all to season to even stand a chance of staying up. We don't have the depth of quality and we have to be realistic in that we are down.
"We haven't shown the technical quality required to hit the target and challenge to win games and that was the case again.
"We had 11 shots - all on target - in our previous home game against Ipswich but that unfortunately proved to be a false dawn."
Coleman saluted Stead for his goal but reserved much of his praise for a miserly City defence after his side's fifth win in six games - and the fourth by a 1-0 scoreline.
Stead powered free of the attentions of Wales international defender Craig Morgan to notch his second goal since on loan from Ipswich.
Coleman said: "Jon showed great determination to get in there and then displayed great calmness to take the chance.
"There was no chance of us taking Peterborough lightly because they are bottom of the league. They have a new manager in who players are keen to impress and we were never going to get it easy.
"We got the battle we expected but, that said, I can't remember us being under too much pressure or our keeper having to make too many saves.
"We have been making a habit of keeping clean sheets lately and a lot of praise for that must go to the defence."
Coventry keeper Keiren Westwood enjoyed a very quiet afternoon.
Wideman Chris Whelpdale was off target three times in the first period and even when Westwood was beaten, Sammy Clingan was on hand to head a Charlie Lee header off the line with a little help from his own crossbar.
Chances were at a premium at both ends, although City striker Clinton Morrison was guilty of squandering a golden opportunity to double his side's lead.
Morrison looked suspiciously offside when being left with a clear sight of goal 17 minutes from time, but keeper Joe Lewis pulled off a fine point-blank save to thwart him.
But one goal proved be enough to send a travelling army of more than 3,000 Sky Blues fans home happy - in stark contrast to Gannon.