A gut-wrenching 31-28 loss in Sydney leaves the Wallabies playing for pride and no silverware in next Saturday's return bout in Wellington.
The coveted Cup will remain in New Zealand for a 23rd straight year regardless of the result at Sky Stadium because the Wallabies need to win a series to get the trophy back.
That's very difficult in a two-match series split in Australia and New Zealand, especially when the Wallabies haven't won across the Tasman since 2001.
A drawn series isn't good enough, as four of Schmidt's predecessors have also learnt the hard way.
All Blacks coach Scott Robertson (R) greets Joe Schmidt after the Test in Sydney. (AP PHOTO)
The Wallabies drew the 2004 series under Eddie Jones, as well as 2007 (John Connolly), 2011 (Robbie Deans) and in 2015 and 2019 (Michael Cheika).
Yet each time the Bledisloe Cup remained in New Zealand, as it will again.
Without outright calling for an overhaul of the rules, Kiwi Schmidt reckons it's a shame the Wallabies have no chance to reclaim the trophy for the first time since 2002 even with a big win in the New Zealand capital.
"I was pretty happy with the arrangement last year and the year before, but now I'm not so happy about that arrangement," Schmidt said when asked if a one-off Test match or three-game series would be fairer than two matches.
"We'd love it to be still alive. I think the people, the public in Wellington (would too).
"It's sold out and it would be a cracking atmosphere but if there was something live on the game, it would be great.
"So that's something that other people make decisions about."
The Wallabies might well have had one hand on the trophy if not for a diabolical start in game one at Accor Stadium on Saturday.
They trailed 21-0 inside 15 minutes after conceding tries to Will Jordan, Rieko Ioane and Caleb Clarke.
Ardie Savea added New Zealand's fourth in the 24th minute but couldn't cross again for the rest of the match, leaving Schmidt and Wallabies captain Harry Wilson frustrated.
"We got close tonight, but not close enough so there's a lot of motivation for us next week," Wilson said.
"We need to start better. We can't really give a team like New Zealand that head start.
"We're really proud of the way we work back into the game and put ourselves in a position where we could have won it there at the end.
"So we took the positive from that but, in saying that we, we just lost to the Kiwis so we've got to be realistic.
Scott Barrett celebrates another Bledisloe Cup triumph with teammates. (James Gourley/AAP PHOTOS)
"We'll take our learnings from tonight and we'll train hard during the week and we'll make sure we come out and be ready to have a red-hot crack there in Wellington."
While All Blacks coach Scott Robertson was relieved his side ultimately "found a way" to win despite bombing seven tries, including three overturned by the TMO, Schmidt conceded the end scoreline somewhat flattered the Wallabies.
"There's not a lot of water in the glass," Schmidt said.
"You lose a Test match so, as Harry said, there's things that we've got to learn from. We can't finish a close second.
"There's some things to be proud about and I totally agree with Harry around building our way back into the game, but giving a New Zealand side a start like that, it's too tough to overcome that."
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