Jon Otsemobor scored a last-minute winner to secure victory for Milton Keynes after Jack Midson had cancelled out Stephen Gleeson's first-half opener for the hosts.
Tensions had been high ahead of the contest but despite fans from both sides entering the field of play to celebrate goals, there were no serious incidents reported and MK Dons now face a trip to Sheffield Wednesday in the next round of the competition.
"I'm tired, it's been a really tough week," said Robinson. "I just thought the game typified two sets of teams with great hunger and passion for the club that they play for.
"I think two teams can walk away from this stadium very proud of each other and that to me is all I wanted.
"I wanted this game to go smoothly, I wanted everyone to conduct themselves in a manner that was right for the English game and I thought we all did that.
"Two sets of fans entered the field of play today, which you can't condone, but what I would say is that not one fan attacked or physically went towards any player.
"I know a lot of people have been criticising us and were expecting something to go on in the game but ultimately today I think that football has been the winner, and that's what I wanted."
AFC Wimbledon manager Neal Ardley feels it is now time for both clubs to move on after they finally met in competitive competition.
"I'm proud of the players. We worked hard on a game plan as we felt it was our best chance of causing an upset and every player carried it out, to a man," he said.
"My main fear was not doing the fans proud in this game and, despite hurting from the defeat, I think we did that.
"It's happened now, both clubs need to move on and AFC need to try and progress and make sure that next time there is a meeting there's not so much of a gulf between the teams."