Mahmoud believes they should be more worried about Jordan and Oman than top seeds Japan and the Socceroos in Group B.
The 29-year-old, who has 101 caps for his country and played a key role in Iraq's 2007 Asian Cup triumph, told reporters that the improving Jordan and Oman were the teams to look out for in the group.
"Some may fear Australia and Japan, but I'm against that and we don't fear anybody," he said. "If we should fear somebody it'd be Jordan and Oman, as they will be facing us aggressively seeking to demonstrate their abilities.
"They are not there by chance, not forgetting to mention also that they are two teams that have improved so much. As for Australia and Japan, they are great teams but so are we."