The two clubs born out of the old Wimbledon FC, FA Cup winners in 1988, met in the second round of the competition at stadium:mk on Sunday.
Jon Otsemobor's injury-time flick sent the Milton Keynes club through with a 2-1 victory after Jack Midson's diving header for AFC Wimbledon cancelled out Stephen Gleeson's superb 30-yard effort.
Robinson told the media after the game: "There was obviously a lot of media attention on both clubs in the build up to the match and it has been a tough week, a really tough week.
"It has been enjoyable but it has also been very difficult as well. I think we are all glad this game has taken its course and we can now move on, I think that is what should happen now.
"All of this has been a good learning curve for me. I have got a dream of being here for a long, long time and know I have got a lot more learning to do.
"This last week has given me a great chance to look at myself and put myself under pressure. If I have offended anybody in the way I have conducted myself, I apologise, but I would do the same again. Maybe I still need to improve but this has all been part of my learning."
The 32-year-old added: "This result, though, was for our fans and the city of Milton Keynes. The criticism this place gets is undeserved and so it is nice to get this game out of the way and to have won."