The Wallabies were embarrassed by the All Blacks in Sydney last week when they were hammered 54-34 but lifted their performance in Dunedin, built on a stinging defence and far more direct attack.
While they blew an early 17-0 advantage, they defended superbly in the third quarter and then took a 29-28 lead with four minutes remaining through a Kurtley Beale try before Beauden Barrett struck back to seal a 35-29 victory.
"We can't be happy with losing," Cheika told reporters in Sydney upon the team's return from New Zealand. "We can be proud of how we performed but we need to make sure that we don't sit down on that and that we keep improving for the next one.
"We can play at this level, it's about being consistent and it's about having the mental aptitude to play at that level all the time, never having a minute off."
The Wallabies now have a week off before they meet a resurgent South Africa side in Perth on Sept. 9, a place where the national side may not be made welcome after the turmoil in domestic rugby this season.
The Perth-based Western Force are battling the national body over the decision to dump the side from Super Rugby next season and local media have reported of a grassroots campaign for fans to wear Force jerseys at the match.
"The Perth test will be really important with what has been going on over there," Cheika added. "It's so important for us to go over there and show them how much the Wallabies want to play for them."
While the Wallabies improved their defence and seized on what opportunities they had as they fed off All Blacks mistakes in the first 20 minutes, they had major problems at the scrum.
They also seemed to drift in and out of the game at times and Cheika was adamant they would need to make sure they do not shut off against the Springboks.
"We have to improve on certain things for South Africa," Cheika said. "We just have to keep building on things, we need to be more consistent and it's just a combination of the big picture and little technique stuff.
"We'll get there."
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)
