He said if they can get it right, the All Blacks should quickly see the benefits.
The pair started together for the first time recently in the drawn test against the Boks in Wellington, with Barrett putting in a performance at fullback which drew strong praise from coach Steve Hansen today.
Mo'unga began more slowly but his value was especially evident after the break when he combined with Barrett to set a tempo the Boks did extremely well to survive.
Asked what he would like to see with his combination with first-five Mo'unga at Perth's Optus Stadium on Saturday, Barrett said: "To work better together."
"I think we've learned a lot from one having one game under our belts," he added.
"At times we were perhaps in each other's pockets. Tactically and structurally, if we can be aligned, it will work best for the team and we should see some good rewards from that.
"He's a cool young guy," Barrett said of Mo'unga, who has led the Crusaders to three titles in three years.
"He's very calm when he speaks. Playing alongside him, there's a great sense of calmness and that's a quality of his that rubs off on the boys in those tough moments when you just need to steady the ship and keep things simple."
"We liked what we saw last time we did it," Hansen said of the Mo'unga/Barrett double act.
"I thought [Barrett] was the best player on the park in Wellington. We just have to make sure we keep providing opportunities. If you look at the footage against South Africa, we did create plenty of opportunities but we didn't finish many of them."
While there will be a sense of the unknown in the Ardie Savea, Sam Cane and Kieran Read loose forward combination, and a little less mystery about the All Blacks' two main navigators, the jury will remain out on the Wallabies' gamble on starting James O'Connor at centre.
O'Connor, who has started a test six years ago and has been plying his trade in Europe, has been used at first-five, second-five, wing and fullback but rarely at centre. His presence may offer attacking opportunities for the visitors, but Barrett and Hansen are of the feeling that O'Connor and the Wallabies will mix things up a bit in terms of their formation.
Barrett said: "Who knows what their midfield combination will present on Saturday? We have to see every phase or play as an opportunity to attack them; it's going to be exciting.
"He's been away for a while and in a jersey we haven't seen him in much. There's no doubt he's a very talented player."