Australia skipper Michael Hooper admits he made the wrong move in not kicking for goal after the Wallabies sunk to a disappointing 9-6 Test loss to Wales.

With the scores locked at 3-3 until the 68th minute, in a dour arm wrestle in Cardiff, Hooper's conceded his decision to go for a try in second half instead of giving Bernard Foley an easy shot at goal was one he should not have made.

After rolling deep into Welsh territory, the Wallabies were repelled by the hosts as Allan Alaalatoa spilled the ball in a maul after a successful line-out from the tourists.

In a similar position soon after, hooker Tolu Latu, who had been solid with his throws to the Wallabies' much-maligned lineout, hitting the target from 10 of his 11 efforts, chose the wrong time to surrender his second turnover of the game.

The chance was lost and the Welsh cleared their lines on their way to a first win over Australia in 10 years.

"If I had my time again I would have gone for the shot," Hooper said.

"I backed the guys and I had wanted to keep the foot on and get the try.

"But my reading of the game there was probably amiss. I should have known the game would come down to penalties in the end.

"Hindsight is a nice factor but I should have gone for goal."

Coach Michael Cheika, who has now tasted defeat in 10 of Australia's past 13 Tests, said he was pleased with the defensive effort from his team but was frustrated at the lack of discipline and number of errors.

"There were too many small errors, whether at the lineout or indiscipline, and they cost us," he said.

"The pressure we built up we released by either infringing or losing the ball at the lineout.

"It was a tight game and this one went against us.

"Those things have happened to us this year and we have got to take that on the chin, understand what we did well and improve the things we didn't do well and get a win next week."

Dan Biggar's late penalty goal was enough to secure victory in the try-less encounter in the Welsh capital watched by about 64,000 fans.

The two sides will meet again in Tokyo next October and organisers will be hopeful of a better spectacle.

Although the Wallabies had more of the ball than the hosts, they struggled in the scrum with New Zealand referee Ben O'Keeffe penalising Scott Sio twice for pulling down Wales prop Ken Owens.

Cheika said he was disappointed by the calls and felt the Wallabies' scrum had been strong against Warren Gatland's huge forward pack.

"I am disappointed with those penalties, they were all called by the touch judge," Cheika said.

"We asked what was happening there. We were clearly domating the scrum but what can you do."