Second-half goals by debutant Francois Zoko and Filipe Morais ensured the hosts progressed to the Southern Section quarter-finals for the first time.
The tie looked to be going to form after a Shaun Williams penalty gave the Dons the lead but Stevenage, who are struggling in League One, were to avenge their 4-1 defeat at stadium:mk last month.
Dons boss Robinson pulled no punches afterwards, saying: "That last 45 minutes was embarrassing. I don't even know what it was - it was a shambles to be honest, a wasted 45 minutes of my life.
"They should have beaten us 4-1 if you want the truth and I'll often defend the lads because I love them to death and I'll fight for them because I want to protect them.
"That wasn't acceptable and they know that.
"There were some of them who gave it a right good go - I thought Dean Lewington was magnificent - but if you look at the way the game goes it was just poor and they need to learn lessons quickly.
"You don't fight fire with fire and we tried to play them at their game.
"We needed to keep playing football and we never did - we reverted to some style that I've never seen us play before and I'm fuming."