Posh, who were third in a group of eight at the start of the day, were undone by Owls striker Korede Adedoyin who scored four goals.
Substitute midfielder Kellan Hickinson did score late on for Posh, but there was still time for Basile Zottos to claim a fifth goal for the hosts.
Posh: Lakin, O’Connell, Fernandez, trialist, Powell, Bojang, Barker, Oluwabori, Gyamfi, Chong, Ishola. Subs: Peters, Laycock, Hickinson, McGlinchey, Ogbonna