Darren Ferguson's men had the ball in the Albion net courtesy of a towering header from recalled Craig Morgan, but referee Steve Bratt cut short their celebrations as he adjudged Morgan to have pushed defender Matt Richards.
Morgan again went close with a header seconds later after Tom Williams delivered strongly from the left before Glenn Murray squandered Brighton's first-half opening when blazing over on the turn after being picked out by a Joe Anyinsah cross.
Chances were few and far between after the break when referee Bratt took centre stage.
The West Midlands official booked six players before departing after 73 minutes apparently suffering from a muscle injury.
Fourth official Paul Barnes took over the whistle with a qualified referee from the crowd overseeing touchline duties as Posh finished strongly with substitute Dominic Green blazing over after Charlie Lee went close with a header.