The Wallabies will finish June sitting fifth in the World Rugby rankings, after a tight series loss to Ireland.
Australia was within striking distance of becoming world number two in Melbourne, but two losses at home to Ireland has pushed the Wallabies down the rankings.
England's third Test win over South Africa has pushed them up to fourth overall, while the Springboks have moved back to sixth.
Wales stay in third place, after their two big wins over Argentina in June, while Scotland regained some ground with their own win over the Pumas last weekend.
France, Fiji and Argentina round out the top 10, with all the June Tests finished for 2018.
The next chance for the Wallabies to move up the rankings will be August's Rugby Championship.
World Rugby rankings, June 25
1. New Zealand - 93.99
2. Ireland - 90.12
3. Wales - 85.94
4. England - 85.68
5. Australia - 84.48
6. South Africa - 83.32
7. Scotland - 83.02
8. France - 79.10
9. Fiji - 76.54
10. Argentina - 75.55