Wales coach Warren Gatland praised his side for showing plenty of courage after they fell short in their brave comeback bid against Australia.
The Wallabies looked out of sight in Cardiff when they led 30-16 midway through the second half, only for the hosts to come storming back in the final quarter.
Wing George North scored his second try which Dan Biggar converted. Wales then cut the gap to just four points when replacement fly-half Rhys Priestland slotted over an easy penalty.
Their hopes of a first win over Australia in nine meetings received a further boost when Quade Cooper was sin-binned late on, but the visitors held on at the end of a pulsating contest.
"It was a great game of rugby if you were a neutral or an Australian. It was a real Test match out there," Gatland said.
"We are knocking on the door. The thing is with the southern hemisphere now which is different to the past is that they are coming here fully loaded and not making changes.
"We dug deep, and we showed courage to come back. Our fitness looked good in the second half, and we put ourselves in a position where we had a chance to win it.
"They (Australia) were smart in the way they played. It was frustrating that of the 18 penalties we got, I think 14 were at the breakdown, which stopped some of the momentum we were trying to create."
Wales had led 13-3 early on before tries from Christian Leali'ifano and Israel Folau helped nudge Australia into a 17-16 advantage at the halfway stage.
They then moved further clear thanks to a try from Joe Tomane, though there were serious question marks over the legality of Folau's final pass to his team-mate.
"We thought it was forward," Gatland admitted.
"The referee (Wayne Barnes) made the decision himself, without the TMO (television match official). I doubt he would have made that decision himself if it was the All Blacks playing.
"He made the call himself. I haven't spoken to him about it. It is not going to change the result."
While full of praise for his players, Gatland acknowledged they need to improve on a record that has seen them beaten in their last 18 Test matches against opponents from the southern hemisphere.
"We are knocking at the door at the moment, and at some stage we are going to knock it over. We were under a bit of pressure, and we kept well in it right until the end," he added.
"We will review a few things in the game, whether we would have made different decisions that might have affected the outcome, but I just thought the last period of the game we looked pretty good.
"As a whole, we are disappointed we didn't win. The players are in good shape, physically, and we've coped with four or five key players not being in the side.
"When these southern hemisphere sides come here they are not picking second-string players, and that's the way we want it. We dug deep today."