United were on the road to Stanley as they looked to continue their excellent start to the campaign.
But they lost out to a late goal as Accrington took advantage of a misplaced backpass to grab the win with just four minutes left to play.
Academy boss Darren Edmondson said: "We created some good chance but the keeper saved twice in one-against-one situations and also pulled off a great stop from a long range shot.
"It's a disappointing end result but we come away with positives to take from the game."
United - Ashton, Goldthorpe (Dixon 60), Brockbank (Miller 75), Olsen (McCarron 60 (Ward 85)), Taylor, Hutchinson, Cowburn, Watson, Lloyd (Kelly 60), Adewusi, Papa.