Australia were at times woeful in defence when they started the Rugby Championship with back-to-back drubbings at the hands of New Zealand before grabbing a first win in seven tests against South Africa last week.
Three tries for the home side in the first 12 minutes on Saturday -- matching their total tally in their first three matches of the competition -- promised a romp, but the Pumas all but monopolised the ball for the rest of the match.
"Got some early tries and then we couldn't get our hands on the ball," Cheika said.
"We know that when we have opportunities we've got to take them and tonight we were able to do that and got five tries.
"Defended better, I still think we could get into our ruck work and our defence a bit better, but improved there and that gave us a bit of a platform to work off.
"It's another little step forward for us."
The match was Australia's last on home soil this year and they travel to South Africa to take on the Springboks in Pretoria early next month before finishing the championship against the Pumas in London.
New Zealand's victory over the Springboks earlier on Saturday combined with the Perth result ensured Australia's reign as southern hemisphere champions was officially ended.
In reality, though, Australia's season has been about damage limitation for quite some time now and Cheika, who has been forced to bed in a string of new players, said he would be looking for further improvements on the road.
"I think we've got to work on our attacking ruck, we lost a few balls there we shouldn't have," he said.
"And we need to get a bit more continuity going in attack but the big thing at the moment has been our (defence) and the set pieces, improving those, and a bit at a time it's coming."
Captain Stephen Moore was also pleased with how well the set piece functioned but it was also the defensive effort that pleased him most.
"I was very proud of the first half when we made close to 100 tackles," he said.
"There was a fair bit of work there. We wanted to finish well, particularly at home. We are on the road now for the rest of the season so we will go again."
(Reporting by Nick Mulvenney; Editing by Ian Chadband)
