"We saw South Africa really lift their game. They really tested us last week and then this game here was always going to be difficult; Argentina in their last home game.
"Even though we weren't great in the first half, we stayed in the game, we trusted our shape and what we were doing and we got the points in the end."
Despite two wins over Argentina being Australia's only successes of the tournament, Cheika believes earning the Puma Cup after retaining the Mandela Plate are important morale boosters for his rebuilding team.
"It is important for them to have a little reward like that," he said.
"We don't delude ourselves that that's the major prize but we want to get to the top and to do that we've got to be consistent and improve.
"We have to step up and improve when we take on New Zealand in a couple of weeks.
"They've got a good attitude and if they can improve their game mindset so there's less variations in the game, then I think we can go further."
The coach was delighted with the performances of international newcomers Marika Koroibete, flanker Jack Dempsey and replacement forwards Allan Ala'alatoa and Lukhan Tui.
The match was eerily similar to the Wallabies' 45-20 win over the Pumas in Canberra, with the score locked at 13-all at halftime and 20-all midway through the second half.
The final score could easily have been the same had Bernard Foley not missed four successive shots at goal at one point.
The five-eighths had slotted 19 straight before losing his rhythm yesterday.
