But Rio Dyer pounced on a smothered Nic White kick to give Wales one last chance of securing their first win against the Wallabies in Australia since 1969.
The hosts slotted a penalty goal to see off Wales’ best efforts, backing up their 25-16 win in Sydney last week.
“Some of the tries were spectacular and were on the back of some really good skill,” Schmidt said.
“I’m just relieved that we’ve got a couple of results because it’ll help build some belief in the players.
“I’m also delighted with the group of men who are really trying to commit to what we’re trying to achieve.
“It’s nice to have clear things to work on.”
The Welsh, who smashed the Wallabies at last year’s World Cup to continue the Eddie Jones-led nightmare, slumped to a ninth straight defeat.
“I’m confident that this team is going to be a really good team,” Wales coach Warren Gatland said. “I can see the signs out there.
“I’ve been clear that we probably need to go through a little bit of pain while we’re in that process of those players getting some more experience.
“I can promise you this is going to be a really good team.”
The scoring couldn’t have been opened in better fashion, with an Andrew Kellaway chip kick setting up a barnstorming run by flanker Fraser McReight.
The Queensland Reds star charged down almost the length of the field, before dishing off to Filipo Daugunu to complete a superb try.
Halfback Jake Gordon’s effort was equally as entertaining, picking up a loose ball and swerving through Wales’ defence in the 24th minute.
Wallabies lock Lukhan Salakaia-Loto was sent to the sin bin for a high hit on Welsh prop Archie Griffin, who was taken off for a head injury assessment.
Melbourne-born flanker Rob Valetini put in a big shift in front of his home fans to be named the Wallabies’ player of the match.
Man mountain Lake was in everything, with the hooker crossing twice in the first half, including via a rolling maul just before the break.
The Wallabies will return to Sydney for a clash with Georgia - who beat Eddie Jones’ Japan this week - next Saturday night, their last Test before the Rugby Championship campaign begins against world champions South Africa at Suncorp Stadium in Brisbane on August 10.