Substitute James Rowe combined with Jake Kirby to net the winner six minutes from time after Ryan Lowe, who opened the scoring, had cancelled out Daniel Powell and Jason Banton's efforts with his second of the game from the penalty spot.
Dons have now won just once in their last six matches in all competitions.
"I am shell-shocked. The players didn't deserve to lose the game but two mistakes have cost us - you have to say well done to Tranmere," Robinson said.
"They have beaten us but other than a couple of missed chances we couldn't have done any more. I will say the officiating wasn't good enough and they can do what they want to me, I don't care.
"The referee has got the rules blatantly wrong over an offside decision that could have given us something from the game.
"Jason Banton was given offside after a Tranmere defender was the last to touch the ball and he was through on goal and that isn't the rule.
"I should be able to come out here and say that he has got the rules wrong. The penalty Tranmere got was a definite one.
"We scored two great goals and theirs were scrappy. The team played very, very well but for whatever reason everything seems to be going against us."
- Sports & Recreation
- Jason Banton
- Daniel Powell