The world's best footballer has helped end Australia's best World Cup, with Argentina ace Lionel Messi scoring in a 2-1 win that eliminated the Socceroos.

Messi hit yet another landmark with a sublime strike and his teammate, Julian Alvarez, later mopped up an Australian mess to score at Ahmad bin Ali Stadium in Doha.

But Socceroos substitute Craig Goodwin, with a speculative long-range shot that deflected into the net in the 77th minute, revived Australian hopes.

Three minutes later, Australia's bundle of energy, Aziz Behich, went on a daring run, tearing through Argentina's defence and, as his eyes lit up when 5m from folklore, his shot was blocked.

Then, in the dying minute, substitute Garang Kuol had a golden chance to level things up, but was denied by a piece of brilliant goalkeeping by Emiliano Martinez, who managed to get his arm in the way before pouncing on the loose ball.

The Australians leave Qatar after their best performance at the World Cup, with two wins in a single edition of the tournament for the first time.

But, just as the only other Socceroos team to advance from the group did in 2006, they depart at the round of 16 phase.

"We gave it everything. Just like we have every minute of this competition. So proud of all the players and the staff. Just not enough on the day," an emotional Jackson Irvine said after the match.

"I think we did everything we could to give ourselves a chance in the game. When Argentina are celebrating like this, victory against Australia, I think it shows what kind of opposition we gave them today.

"It's difficult to comprehend everything at the moment. It's all quite raw. I hope we made everyone proud."

Coach Graham Arnold said he was proud of his players, but admitted the Mat Ryan mistake that led to the Alvarez goal had cost the team.

"I have to be very proud of the players. You know, we played against the number three in the world. And the first goal from Messi was a quality goal. The (Ryan) mistake cost us," he said.

"I just hope that everyone back in Australia really respects what we've done and are proud of us as well. We took it to them."

Harry Souttar, who has been one of the defenders of the tournament, said he was gutted to be out of contention.

"Just really gutted for the lads. I think you saw how much it means to us," Souttar, who is likely to be chased by several EPL clubs after his performance, said.

"How much effort we put in. Yeah, we took it right to the end. What can I say, they're a world class team. Simple as that.

"They've got world class players that can turn it on an instant, like you saw with the first goal.

"We're gutted. We're so disappointed. But I think we can be proud of ourselves and the journey that we've had."

Messi's ninth World Cup goal, and first in the knockout stages of the showpiece tournament, books Argentina a quarter-final against the Netherlands.

The Socceroos were willing but unable to control the brilliant Argentine and his teammates, who largely toyed with the outclassed Aussies in the first half.

Messi's mob were akin to a prize fighter examining the weakness of their opponent before landing a knockout blow.

It came in the 35th minute when captain Messi started, and finished, an attacking chain.

Darting inside with intent from the right flank, Messi played a sideways pass to teammate Alexis Mac Allister who delivered, one-touch, to Nicolas Otamendi.

In a twinkling of Otamendi's toes, he played back to Messi and with his golden left foot the megastar split three Australian defenders with a shot that gave goalkeeper Ryan, diving to his right, no chance.

The Socceroos, ranked 35 slots lower than the world number three Argentines, rarely ventured forward in the first half.

Behich, who irritated Messi with a jumper tug in a first-half flashpoint, charged into the Argentine box after an insightful Irvine pass in the 19th minute.

But the Socceroos' first forward sortie ended with Behich squeezed over the by-line with the only other glimmer coming from a Souttar header that was cleaned up and away by Argentina.

Argentina doubled their advantage in the 57th minute after an Australian calamity when captain Ryan, receiving a Kye Rowles back-pass, took a heavy touch and two Argentines charged.

Ryan tried to escape the pending danger with his right boot but the ball escaped his control: Alvarez pounced and slotted into the vacant net.

The Socceroos, 20 minutes later, were given a lifeline when Goodwin fired from 20m out and found the net.

With a more attacking set up for the final throes of the game, both Australia and Argentina had chances to score again, with Kuol's opportunity the best chance to tie up the match, only for Martinez's brilliance to keep the Socceroos at bay.

AAP/ABC