Posh's defeat saw them drop out of the play-off places and continued an abysmal run of away form as they have taken just one point from their last eight away trips.
The club gave a blanket "no comment" at the end of the game, with Ferguson refusing to send out any of his coaching staff.
Oldham produced an amazing second-half comeback to stun Posh at Boundary Park, with the winner coming from Genseric Kusunga in the fourth minute of stoppage time.
Peterborough scored twice in the first 25 minutes when Britt Assombalonga converted Mark Little's cross and Tommy Rowe steered in a near-post header.
The visitors made it 3-0 at half-time as Lee Tomlin stroked in from 14 yards and Oldham - with only one victory in nine previous games - looked dead and buried.
But Gary Harkins launched the fightback from close range and David Worrall added Oldham's second with a fine strike before Posh made it 4-2 in the 63rd minute when Nicky Ajose punished a defensive blunder.
Johnson's side levelled the scores through James Wesolowski and an 89th-minute penalty by Harkins after Tomlin handled on the line. The Posh striker was shown a straight red card.
The clinching goal came after more chaotic defending by Peterborough, with Kusunga blasting in from two yards.