Australia coach Graham Arnold wants his squad assembled in Dubai by December 27, meaning Rogic will miss Celtic's clash with Rangers two days later.
And Sutton has hit out at the decision, saying the Socceroos shouldn't need Rogic to beat Jordan in their Asian Cup opener.
"What has upset me is the Rogic situation and him not being able to play against Rangers," Sutton said on BT Sport.
"Australia have got Jordan in the Asian Cup.
"They don't need Tom Rogic to bump Jordan. Absolutely not.
"It's not right. There are a lot of Scottish football fans thinking the Socceroos should shove their XXXX somewhere the sun doesn't shine.
"It's not on! It's Mickey Mouse football. Stick to your prawns and your BBQ's Australia."
Socceroos trio Martin Boyle, Jamie Maclaren and Mark Milligan are in the same boat as Rogic, as they look set to miss the Edinburgh derby on the same day as the Old Firm clash.
As well as Jordan, Australia will take on Palestine and Syria in the group stage of the Asian Cup.
