Reece Hodge missed a last-gasp penalty that would have won the game as Australia drew with a weakened Argentina on Saturday, a result that rubber-stamped New Zealand as Tri Nations champions.
The match ended 16-16, a fortnight after the two teams played out 15-all draw with Hodge also missing a penalty in the dying seconds of that clash.
The Wallabies needed to earn a bonus point and crush the Pumas by an unlikely 101 points to overhaul the All Blacks in the tournament's final game, while Argentina needed to win by 93 points.
Australia captain Michael Hooper said: "We're not happy with the performance, we're disappointed we can't get a win in our last game.
"They are a tough cookie to crack, they apply pressure really well. It has been a long, tough season – it has been great to salvage some Test matches and get some Aussie crowds.
"It was hard conditions, we were smart with our kicks and won the territory battle, but were unable to convert.
"There were some nice parts, some good wins and performances from individuals this season."
Argentina's rollercoaster ride of a tournament hit a low this week when historical racist social media posts were unearthed, costing the Pumas the services of their inspirational captain Pablo Matera and two other players for the match.
They appeared to have brushed aside the tumultuous events of the week, however, and looked on course to round out their campaign with a victory when a Bautista Delguy try helped them to a 13-6 half-time lead.
Hodge kept Australia in the hunt from the kicking tee but lock Lukhan Salakaia-Loto looked to have stopped Australia's comeback in its tracks when he smashed into the jaw of Santiago Grondona and was red-carded.
A Dominic Miotti penalty extended Argentina's lead to seven points soon afterwards but numerical parity was restored when Lucas Paulos was shown a yellow card for collapsing a maul.
Australia immediately rolled another maul across the line with Hooper awarded the try to level up the scores in the 67th minute.
Twelve more minutes of attritional rugby played out on a rain-soaked pitch had passed before a penalty was awarded to the home side and all eyes turned to Hodge.
The versatile back had watched a potential match-winner come back off the post in Australia's first Test of the season, a 16-16 draw with the All Blacks in Wellington.
He was to have no more luck against the Pumas in Newcastle two weeks ago from 40 metres and a shorter kick from a worse angle again proved beyond him on Saturday.
Argentina scrum-half Felipe Ezcurra said: "We made a really good first half of the match and Australia a really good second part, so it was a draw.
"It is beautiful [to be able to play] – we had a really tough year with a very long quarantine. To play these games is a really, really good thing for us."