“At 22-0 down after the first quarter, there was real courage again from the players,” Schmidt told South African TV channel SuperSport.
“We were forced to play catch-up and take a few risks, and there were a few lucky bounces for us, so we are not going to get too carried away.
“But at the same time I am incredibly proud of the group. I am realistic about getting a little bit of luck, but delighted we came back. 1963 was a long time ago, so the players are delighted.”
Argentina host New Zealand later on Saturday in Cordoba.
South Africa: Nche, Marx, Louw; Etzebeth, De Jager; Van Staden, Du Toit, Kolisi (c); Williams, Libbok; Arendse, Esterhuizen, Kriel, Van der Merwe; Fassi.
Replacements: Mbonambi, Venter, Ntlabakanye, Mostert, Smith; Reinach, Moodie, Willemse.
Australia: Slipper, Pollard, Tupou; Frost, Skelton; Hooper, McReight, Wilson (c); White, O’Connor; Pietsch, Ikitau, Suaalii, Jorgensen; Wright.
Replacements: Paenga-Amosa, Bell, Nonggorr, Williams, Gleeson; McDermott, Edmed, Kellaway.
