Wales trailed 17-6 in the first half but rallied strongly and looked to be heading for a win when a Martyn Williams try gave them a 26-17 lead.
The Wallabies fought back with tries from Cameron Shepherd and man-of-the-match Chris Latham, and Wales needed a James Hook penalty to salvage a draw.
"At times I thought we were going to win it and at times I thought Australia were going to win it," captain Thomas said.
"Every time we play Australia we are improving, and I hope that when it comes to the World Cup match it will be a classic."
Wales and Australia have been drawn together in Pool B for next year's Rugby World Cup in France and are due to meet in Cardiff on September 15.
Australia captain Phil Waugh and Latham were frustrated that the Wallabies, who were well on top for most of the first half, had allowed their hosts back into the match.
"It's very disappointing," said Waugh.
"The Welsh punished us for the mistakes we made, and so credit to them."
Australia had the put-in at a scrum in Wales territory with the scores tied at 29-29. But the Wallabies pack was turned, and possession squandered.
"We let ourselves down losing the scrum," said Waugh.
"It's just the simple things, and we've got to go away and work on them."
Latham said: "To be honest it's disappointing. We came over here saying that we wanted to win all seven games of the tour.
"Now we've got to have a look at our games as individuals and go from there."
Australia dominated the opening half hour and raced into a 17-6 lead with tries from Shepherd and Matt Giteau.
But Wales launched a courageous comeback and opened a nine-point lead with tries from Shane Williams and Martyn Williams either side of half-time.
Australia surged ahead again with Shepherd's second try and a dazzling solo effort from Latham.
But once again Wales refused to be beaten - and Hook, making his home debut as a first-half replacement for the injured Stephen Jones, landed the penalty which ensured a share of the spoils.