York led their opponents by just one point in the table before kick-off and took the lead thanks to Michael Coulson's header after 41 minutes.
The Minstermen should have doubled their advantage after the break only for Ryan Bowman to miss an open goal, but AFC Wimbledon failed to take advantage of the mistake.
In truth, the Dons were second best throughout and could have easily lost by more, failing to register a shot on target and leaving Ardley fuming.
"I've just told them in there that it's not good enough. It's so far from good enough it's ridiculous," he said.
"We've got three days to get ourselves together. There won't be many players who can knock on my door this week.
"We prep really well for these games and I feel let down personally, and that's not me passing the buck, I'm the manager of the football club but I can't win the battles on the pitch for the players.
"We gave the ball away nearly every time we got it. We moved the ball too slowly, we were nervous in the way we played, which seems to be a common thing at home and I don't know why.
"When we did play around them and get our spare man in, we came backwards.
"The goal is a ludicrous decision from the referee. He's tripped our player up and then given them a free-kick. That's why I was furious and he knew it. It's up to us then to defend the second phase and we didn't do it."