Posh boss Darren Ferguson handed a debut to Portuguese defender Ricardo Santos, who arrived from non-league Thurrock in February. That was one of eight changes he made for the clash.
Another non-league acquisition, Kyle Vassell, failed to take the hosts' best chance.
Vassell was denied by the legs of Vale goalkeeper Sam Johnson on the half-hour after taking too long to get his shot away. He then turned provider when Josh McQuoid sent a snap-shot just over the crossbar on the stroke of half-time.
Vassell saw another effort deflected wide early in the second half before a third opportunity was snuffed out by a block.
Posh, who will play Leyton Orient in the play-offs, were much improved following a double substitution which saw Joe Newell and Danny Swanson arrive from the bench, but they could not manage a breakthrough.
The same applied to Vale for whom Jennison Myrie-Williams posed the biggest threat. He twice tested Posh keeper Bobby Olejnik with curling efforts early on but then blazed a glorious opportunity over the bar with 18 minutes to go and was promptly replaced as visiting boss Micky Adams handed a farewell appearance to the retiring Chris Shuker.