Barr is lined-up to build the 21,000-seater stadium in the Loirston area of the city.
The Dons were hoping a new Calder Park community sports centre at Cove would double as a training facility for the club next to the new stadium.
But Aberdeen City Council has rejected plans for the training centre and decided to to take control of the land to look into other development opportunities in the area.
Aberdeen FC Chairman Stewart Milne said: “Disappointment and frustration do not come close to how my colleagues and I are feeling right now.
“As was made crystal clear, the Calder Park development has been designed as part of the master planning exercise to be completely integral with the new AFC stadium at Loirston and this decision has effectively also killed off that development.
“Without wishing to scaremonger in any way, the implications of this completely illogical verdict could have major implications for both AFC and indeed Cove Rangers and right now, the Board require some time to discuss both the consequences of the judgement and what our next move is likely to be.”
The club had planned to move from Pittodrie to a new ground at Loirston Loch, on the southern outskirts of the city, for the start of the 2014-15 season.
A council spokesman told the BBC: “There’s no decision that directly pertains to Aberdeen Football Club that was made yesterday, and there’s a lot of room for discussion and I’m very optimistic that we can produce an outcome there that can satisfy people.”