The Cardiff Blues wing cut a crestfallen figure as Wales saw their hopes of claiming a rare win against top southern hemisphere opposition wrecked by Wallabies star Kurtley Beale's try with 26 seconds left.
It means that Wales will go into Monday's 2015 World Cup pool draw in London as a third-tier nation after they dropped two ranking places.
"It is gutting," Cuthbert said.
"We put so much effort into that game, so to come away with a loss in the last minute is pretty heartbreaking.
"We felt comfortable throughout the whole 80 minutes. We went in front, but it all got a bit loose in the final minute and they scored in the corner.
"It is definitely the worst I have felt after a game. I felt bad after the second Test in Melbourne in June, when we lost to the last kick of the game, but this is a kick in the teeth even more.
"It is just so frustrating. We have got the physicality and calibre of players to compete with the world's best, I think it is just that mental edge, maybe, and that little bit of luck."
Centre Jonathan Davies has no doubt that Wales can make a strong RBS 6 Nations title defence despite experiencing their worst losing run for 10 seasons.
Wales' next game is a Six Nations opener against Ireland in Cardiff on February 2.
But they will head into it on a demoralising sequence of seven successive defeats and no victory over a Test-playing country since last season's tournament when they beat France to clinch the Grand Slam.
"We have just got to make sure we look forward to a big Six Nations," said centre Davies, following autumn losses to Argentina, Samoa, New Zealand and Australia.
"We are defending champions and that is the way we must think. We've got to have some confidence about us and not be down on ourselves."
Wales full-back Leigh Halfpenny, meanwhile, was discharged from hospital yesterday after being hurt during the dramatic closing seconds against Australia. He had earlier kicked four penalties to put Wales within sight of victory.
Halfpenny, 23, was taken to Cardiff's University Hospital Wales, where he underwent scans after complaining of neck pain, but any serious injury has been ruled out.
"I want to say thank you to all of the medical teams who have looked after me following my injury," he said.
"The paramedics, WRU and Millennium Stadium medical teams were outstanding. All of the staff at University Hospital Wales were also amazing.
"Everyone has been so supportive, and the care that I have had has been incredibly professional and second to none."
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