Friday's failure initially prompted APA to publicly concede defeat.
Hours later, however, it began backtracking when a major US investment fund decided shortly after the deadline to partially back the deal, pushing acceptance to 50.6 per cent.
Getting 50 per cent support would have given APA a two week extension to secure the 70 per cent backing it needed to seal the deal.
But on Sunday Australia's Takeovers Panel, a body empowered by the Australian Securities and Investments Commission to rule on buyouts, refused to count the late acceptances.
APA immediately appealed the rejection, but early on Monday the panel ruled that the decision would stand.
"Discussions with regulators since the Friday deadline under APA's offer have not resulted in APA being able to include a late acceptance which would have resulted in a two-week extension of APA's offer," APA said in its statement on Monday to the Australian stock exchange.
"In view of the fact that a majority of Qantas shareholders lodged acceptances for APA's offer, APA is exploring a number of alternatives including the possibility of making a renewed offer for Qantas at A$5.45 per share," it added.
Qantas announced a temporary halt to trade in its shares before trading resumed on Monday morning amid predictions the price would plummet and growing calls for the airline's chairwoman, Margaret Jackson, to quit for backing the failed deal.
Several analysts said members of the Qantas board had been irrevocably compromised for backing a bid that was rejected by more than half the company's shareholders.