Celtic manager Brendan Rodgers was desperate to retain his star midfielder's services, but he was ultimately unable to persuade Football Federation Australia.
Given FIFA require clubs to comply with the rules regarding a player's international call-up, the Scottish giants faced a slim chance to sway the consensus.
As a result, the 26-year-old - alongside Hibernian trio Mark Milligan, Jamie Maclaren and Martin Boyle - will now travel to Dubai for the AFC Asian Cup, with Rogic revealing he "did everything in my power to stay".
"I'm very disappointed to be missing the game on the 29th," Rogic wrote via Instagram.
"A decision has been made but I did everything in my power to stay for the match.
"I am a proud Australian but also love my club. It should never have been a debate between playing for club or country, ideally it would have been for both.
"Another challenge awaits in the Asian Cup, where I will give my all and proudly represent my country."
The Socceroos will face Jordan in the opening match of their Asian Cup campaign on January 6.
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