Sutton was scathing of the Socceroos after they insisted Rogic miss Celtic's clash with Rangers – which Rangers won 1-0 - as he felt the attacking midfielder could have joined Graham Arnold's side in camp late given the importance of the Old Firm derby.
"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," Sutton said on BT Sport last week.
"It's not on! It's Mickey Mouse football. Stick to your prawns and your BBQ's Australia."
And after the Socceroos defeated Oman 5-0, Sutton was at it again, posting on Twitter: "Well done Socceroos for beating the mighty Oman and leaving Tom Rogic out of the squad..."
The former Chelsea and Celtic striker was mocked by his fellow BT Sport pundit Robbie Savage, who appeared to revel in Sutton's disappointment after Celtic's loss.
Australia will open their Asian Cup title defence against group rivals Jordan on Sunday.