The Latics squandered a gift-wrapped opportunity to snatch a deserved draw when staging a rousing late fightback. They trailed by two goals entering stoppage time but substitute Charlie MacDonald nodded his first for the club from point-blank range after being picked out by a terrific Connor Brown cross to raise hopes of an unlikely point.
And that is exactly what they should have earned as defender James Tarkowski contrived to miss an open goal with the last kick of the game after a James Dayton corner had been headed towards the target by debutant Joseph Mills.
Record signing Britt Assombalonga had earlier delivered a stellar display to put Posh on course for victory, breaking the deadlock with a scorching 25-yard strike and then winning a penalty which Lee Tomlin converted.
Johnson said: "We showed again that we are not frightened of teams in this league.
"We kept going to the very end, got a good goal back and how James missed at the end I will never know.
"We probably did enough to deserve a draw and on another day could have won the game.
"Aside from conceding a couple of poor goals it was a really pleasing performance.
"There is a right way and a wrong way to lose games of football - and this was the right way."