A brace apiece from Will Grigg and substitute Benik Afobe secured a famous and crushing win for the League One outfit, humbling Louis van Gaal on his first taste of the competition.
The defeat compounds Van Gaal's stuttering start to his reign at Old Trafford and the former Netherlands coach remains without a competitive win.
But Robinson was quick to point out the plethora of positives for his side, who reached the third round for just the second time since their move to Milton Keynes in 2004 in front of the stadium:mk's first sell-out crowd.
"We spoke before the game about their quality. The first 15 minutes, we found it difficult and looked disjointed but the players turned it round," he told Sky Sports.
"I'm a little bit in shock... it's ridiculous and something dreams are made of. We've got two strikers fighting for the number nine shirt and they both scored twice each.
"They've set standards they now have to live up to. My players and my football club, and the city in general, deserve credit tonight.
"Manchester United are massive, people will always want to pick bones in their side but my players deserve an awful lot of credit.
"We worked hard all week, sometimes you work hard and don't get what you deserve but the players did really, really well. It has been a perfect evening."
