Schmidt's side, inspired by free-wheeling substitute fly-half James O'Connor, nearly pulled off a miraculous comeback on Saturday, piling on 19 points in the final 13 minutes at Allianz Stadium.
But unlike last week's last-gasp win in Townsville, Australia couldn't conjure up a knockout blow in Sydney on Saturday.
The Wallabies picked up two bonus points in the narrow defeat after scoring four tries to Argentina's one and will enter the penultimate round of the Rugby Championship top of the table with a 2-2 record.
But while Australia may sit in first place, the path ahead is fraught with danger.
The Wallabies will face an All Blacks side at Eden Park on September 27 smarting from a 43-10 loss to South Africa on Saturday, before a home Test at Perth's Optus Stadium on October 4.
If Schmidt's side are to trouble New Zealand on the road at a Test venue where they have dominated for 30 years, they will need to fix up their discipline.
Australia gave away 14 penalties to Argentina's seven and struggled to build pressure.
"I'm dominated by disappointment," Schmidt said.
"We had enough of the game to get the result, but a lot of it was our own errors.
"Argentina are a really good team, but when we're making 11 line-breaks to three and scoring four tries to one and we don't get a result? It's incredibly frustrating and disappointing.
"We would stack some good work together and then cough the ball up or give it away too easily."
Argentina fly-half Santiago Carreras made Australia pay for their ill-discipline, kicking seven penalty goals from seven attempts.
Carreras had got the Pumas on the board with a second-minute penalty, before Joseph-Aukuso Suaalii powered his way over the line shortly after to put the Wallabies in the lead.
Tane Edmed, in his first Test start at fly-half, converted Suaalii's try but then brought his work undone when a free kick was charged down and pounced upon by captain Julian Montoya for Argentina's only try.
"That will be a big learning curve for a man who worked his socks off," Schmidt said of Edmed's blunder.
"We didn't get the continuity of the ball for him to bring us into the game, so it was pretty tough for him."
Australia did well to survive a period when they were down to 14 men after winger Max Jorgensen was sin-binned for a knockdown in the 18th minute.
Carreras, who had converted Montoya's try, kicked three more first-half penalties to give Argentina a 19-7 halftime lead.
The Wallabies failed to heed the lessons of the first half and watched on as Carreras guided two more penalties through the posts.
Needing a change of pace with his side down 25-7 after 55 minutes, Schmidt brought Edmed off for O'Connor.
Suaalii and O'Connor combined to send Andrew Kellaway over the line, before the veteran playmaker helped set up Filipo Daugunu for a second try in the space of two minutes as Carreras watched on from the sin bin.
Daugunu scored a minute from time off a certain forward pass that had Argentina coach Felipe Contepomi blowing a gasket.
Thankfully World Rugby's blushes were spared as Australia failed to conjure a try in the final phases, the Wallabies conceding a penalty deep in their own 22m to finish the match.
Schmidt remains unsure if O'Connor, set to link up with English club Leicester in coming weeks, will be available for the Wallabies' encounters with the All Blacks.
"I will definitely be having a chat to James this evening or tomorrow morning because we have to make a decision pretty much straight away," the coach said.
