The Cod Army were made to rue their missed chances after Jonson Clarke-Harris’ gut-wrenching 89th-minute winner at Highbury.
Grayson was quick to take the positives after matching a side which had put seven past Accrington Stanley last time out.
Town’s players had one eye on a late play-off push but they are now 10 points behind local rivals Blackpool with just eight games left.
“There will be other occasions where we’ve played not as well as today and won the match, that’s just how it goes sometimes,” reflected Grayson.
“Have my players given everything, have they worked hard and carried out the instructions that I’ve asked them to do? Yes, there will be a lot of boxes ticked but unfortunately we’ve got nothing out of a game we deserved something from.
“I thought we did a lot of good things, to be fair.
“We competed against a strong team that are at the top end of the division, we kept them quiet and Alex (Cairns, keeper) really only had one save to make.
“I think we competed really well against a strong team. People like Jonson Clarke-Harris and Sam Szmodics are a real handful and we contained them really well.
“We wanted to keep going because we wanted to try to get towards the play-offs.”
Ged Garner and Wes Burns blew Fleetwood’s best chances at the end of the first half, and after Sam Finley forced a fine save from Posh keeper Christy Pym, Danny Andrew hit the bar for the hosts in the second period.
On another day Fleetwood could have been out of sight long before Clarke-Harris popped up with the winner.
Consequently, Grayson challenged his charges to be more ruthless in the final third between now and the end of the season.
He admitted: “When you look at our chances, we’ve hit the bar, we had some other close shaves.
“We were quite happy with how we played and how we created chances, but when you concede so late on, it’s obviously frustrating. I don’t think we deserved that.
“We are just slightly disappointed that, at the top end of the pitch, we weren’t as ruthless as we might have been.
“That’s not just the strikers, it’s the final pass or the final shot or our decision-making.
“These are just small points we want to improve on week in, week out.
“If you ask me if I’m happy with the players’ attitude and application, then I certainly was because we did everything apart from put the ball in the back of the net.
“We had two free-kicks from the same position as the one they scored from.
“One of ours went past the post and the other hit the wall so it’s these fine margins in football.”
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