The Dons were playing their 500th competitive fixture since the club was formed in June 2004 and marked the occasion with a 2-0 win over their local rivals to ensure their place in Saturday morning's second-round draw.
The men from Milton Keynes were patient in the first half, in which the visitors had Ishmel Demontagnac shown a straight red card, but turned on the style after the break as Patrick Bamford and Dele Alli scored the goals.
Robinson said: "It was a good night for us, it was a local derby and it gives the fans some bragging rights too.
"It was nice to put on a performance on a night like this, it was important to me and they didn't let me down. I'm pleased we didn't let the fans down, so that's for them.
"We had the chances to win put the game out of sight in the first half but we never took them, everyone was on the edge of their seats in the second half but I thought it was a very professional performance from the players."