York boss Nigel Worthington remains adamant City can avoid the drop despite tasting defeat in his first game at the helm.
Midfielder Harry Pell netted 11 minutes from time as AFC Wimbledon climbed from bottom to 21st in the League Two table with a 3-2 success.
Chris Smith had earlier twice clawed York back, equalising shortly after Mat Mitchel-King's strike in the 21st minute and Brennan Dickenson's on the hour, but it was not to be and the Minstermen now sit just two places and a point ahead of the Dons.
"This is a learning curve and a lot of things we need to learn very quickly. There's one or two things we've got to continue to work on and improve on," Worthington said.
"These next nine games are all about mental toughness, individually and collectively, and the situation stares us in the face. It's how you deal with it that counts. You can fight it or buckle.
"I would like to think there's enough in there to get the points required. There's no sympathy in the game and we know that.
"The spirit is very good, they're together and I'm very pleased with that. It's just mistakes cost goals and there's some little mistakes we have to tidy up on.
"The player's participation was outstanding; they kept going right until the very end which showed a lot of character.
"I was delighted with that. If you score two goals away from home you usually get something out of the game."