A weakened Australia gave up a 15-point lead midway through the third quarter, losing 91-83 in their final Group D clash.
Later in the day, Slovenia suffered a 67-64 loss to group winners Lithuania to finish second.
But, by finishing third, Australia moved further away from the United States in the knockout rounds.
If Slovenia beat the Dominican Republic in the round of 16, they will face the USA in the quarter-finals while Australia cannot meet the tournament favourites until the last four.
Dragic, who plays for the Phoenix Suns in the NBA, said FIBA should take action.
"Basketball is a beautiful sport, there is no room for fixing the game like today Australia vs Angola!! @FIBA should do something about that!" Dragic tweeted.