Posh condemned fierce rivals MK Dons to a first league defeat of the season despite having defenders Nathaniel Knight-Percival and Mark Little dismissed.
Knight-Percival walked after just seven minutes after appearing to catch Patrick Bamford with a hand to the face, while Little was red-carded with a quarter-of-an-hour remaining for a crude challenge on Dean Lewington.
The second dismissal arrived moments after Dons substitute Izale McLeod had halved the arrears when pouncing from close range, but that was the only breakthrough the visitors could manage as Posh produced a stunning backs-to-the-wall effort to pocket the points.
Robinson said: "The referee got a lot wrong.
"Their penalty should never been given as their lad handled the ball just before he went down - and he missed a blatant spot-kick for us.
"Peterborough are as good as it gets at this level of football and I don't think we could have done anymore to win the game.
"We had 36 efforts on goal, but their goalkeeper had the game of his life and we didn't have that bit of luck on our side.
"This result will be really hard to accept for the next 24 hours, but we will learn lessons and move on as we always do."
The hosts had hit the front when Lee Tomlin converted from the spot in the 14th minute after a marauding Danny Swanson run had been illegally ended by Shaun Williams.
Dons men Jon Otsemobor and Bamford both fluffed glorious chances before Posh doubled their advantage when top-scorer Britt Assombalonga thumped his eighth goal of the season from a difficult angle in the 33rd minute.
Dons dominated the remainder, but were frequently frustrated by inspired Posh goalkeeper Bobby Olejnik.
The pick of his many super saves arrived when he tipped a long-range blast from George Baldock on to a post and even when Olejnik was beaten, skipper Tommy Rowe was on hand to nick the ball off the head of Bamford as he looked sure to score.
Posh manager Darren Ferguson said: "I'm not going to speak about the referee as I don't want to deflect any attention from my players.
"All I would say is that it is rare for one team to end up with two red cards and four yellow cards in a derby while the opposition don't pick up any."