As a result New Zealand had to be content with ninth place after missing the knockout phase for the first time in tournament history.
The tournament was New Zealand's second after its delayed return due to the Covid pandemic, was played in stifling heat.
With two rounds of the 2021-22 series left, Argentina leads the competition on 118 points. South Africa are second on 116, with Australia third on 110, and Ireland fourth on 88, one point ahead of Fiji, who also missed two tournaments.
The All Blacks Sevens are in 11th place on 39 points, having missed the first four tournaments.
The next tournament is in London at the weekend, with the final round in Los Angeles on August 27-28.
Earlier, New Zealand beat Scotland 42-7. But, it was their 14-29 loss to Australia in pool play that finally undid their chances. That margin, and the USA's 28-12 win over Scotland denied them in the end.
Australia scored tries to Henry Hutchison and Ben Dowling in the first four minutes before Leroy Carter got on back in the seventh minute. However, Australia responded immediately with Corey Toole scoring. That was followed after 10 minutes by Dietrich Roach. Amanaki Nicole scored a consolation try for the All Blacks Sevens a minute from the end.
They were not alone as South Africa also missed out on the quarterfinals after they suffered an opening game 12-21 loss to Ireland and then a third round 7-19 loss to Samoa.
Ireland carried its form through to beat France 24-7 to reach their first final, against Fiji, going down 17-29.
New Zealand beat Scotland 19-0 and the United States 19-17 in their other pool games.
Then, on the final day, they beat Wales 28-0 in their quarterfinal playoff for ninth place. Brady Rush scored two tries, Akuila Rokolisoa and Roderick Solo one each, and Spain 36-7 in the semifinal with Regan Ware and Caleb Tangitau scoring two tries each and Joe Webber and Ngarohi McGarvey-Black scoring one each.
In their ninth place final with Scotland, Tangitau and Rokolisoa crossed twice each, while McGarvey-Black and Dylan Collier also scored.