Meanwhile, striker Aaron Mclean remains available after putting in a transfer request before Christmas.
George Boyd, Shaun Batt or Ben Wright could partner Aaron Mclean in his absence.
And it should have been a much greater margin, with Mackail-Smith and Aaron McLean both hitting the bar.
Striker Aaron Mclean is on the transfer-list by request, but Cooper is hopeful he will reconsider his position.
Craig Mackail-Smith, Joe Lewis, Aaron Mclean and Lee Frecklington have each been linked with moves away from London Road.
It has been a turbulent week at London Road with striker Aaron Mclean having a transfer request accepted by the board.
But the Posh's pre-match preparations were not helped by the loss of strike trio Aaron McLean, George Boyd and Craig Mackail-Smith to a virus.
Posh started the game with Aaron Mclean and Ben Wright leading the line, but introduced George Boyd and Shaun Batt as the match wore on.
Hull had been the more impressive side for much of the game with Matty Fryatt heading wide before Aaron Mclean's shot was parried away by Jason Steele.
Posh rallied before the interval but Aaron McLean shot wide from 20 yards and Tommy Rowe had a shot blocked after another long Geohaghon throw-in caused chaos.
Midfielder Paul Coutts has been linked with rejoining former boss Ferguson at Preston North End, while striker Aaron Mclean has been transfer listed at his own request.
Wright is currently the club's third choice striker behind Aaron Mclean and Craig Mackail-Smith, and admits he faces a battle to win a regular place in the side.
Gabby Zakuani and Mark Little should both be fit after returning to training, but Chris Whelpdale, Aaron Mclean, Izale McLeod, Liam Dickinson and Nathan Koranteng are all out.
"Rather than to sell, I'd prefer a fully focused Aaron Mclean who wants to go out and put a shift in because we can't afford anyone better, " he said.
Aaron Mclean is struggling with a virus and may have to settle for a place on the bench having been taken off at half-time in the Cardiff match on Monday.
Posh already have three proven strikers on their books in the shape of Aaron Mclean, Craig Mackail-Smith and new signing Dave Hibbert, so will not be desperate to bolster their attacking options.
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