The semi-finals of the national knock-out cup competition were slated for September 13-14 but FA issued a notice on Monday saying they had been brought forward by two weeks.
With Auckland playing an away semi-final against Heidelberg United in Melbourne on Saturday, the New Zealand A-League team said their pre-season plans were thrown into disarray and they had to scramble to arrange accommodation and training venues.
Corica, a twice A-League title-winning coach, said FA made the switch in part because their semi-professional opponents had an end-of-season trip planned.
"We weren't expecting (the switch), but in the end we had no choice," the Australian told New Zealand media on Friday.
"They decided to play it Saturday, because Heidelberg had some stuff going on with the finals coming up, and then are going away on an end-of-season trip, that's the reason we can't play them later."
Heidelberg are scheduled for a playoff match on September 7 in the second-tier National Professional Leagues (NPL) competition.
The NPL's title-deciding Grand Final for Victoria state is slated for September 14, which would have clashed with the original Australia Cup semi-finals schedule.
FA and Melbourne-based Heidelberg did not provide immediate comment when contacted.
Corica said his team had "got the raw end of the deal" and players' plans for an off-season break had been put on ice.
"I felt a bit sorry for the players, they had to tell their families they were not coming back for another few days," he said.
"I would say it is unlucky, but it's not – it is poor planning really, the decision Football Australia has made."