Roared on a by a tremendous 800-strong travelling army, the Dons enjoyed the better of a largely disappointing first half.
Substitute Kevin Sainte-Luce won the game with 10 minutes left as he drilled home from 25 yards after Chris Hussey's corner-kick was not sufficiently cleared.
Still said: "For some reason we just couldn't get going.
"There was too much edginess out there and in the end we've been punished for putting in a poor performance.
"We just didn't work their keeper nearly enough.
"Wimbledon have been going well of late and we knew we were in for a tough game, but we've not been anywhere near competitive enough.
"In a big home derby fixture like this I was looking for more. There was a good turnout from the supporters but they'll be going home really disappointed with an outcome like that."