The Kiwis did well to absorb plenty of early pressure from the hosts and came back from an 8-0 deficit after 14 minutes with Kevin Proctor's converted try putting them within two points at halftime.
But Barnett questioned the side's tactics after the break with captain Jesse Bromwich and Taumalolo remaining on the interchange bench as the Kiwis dropped their intensity and struggled for go-forward throughout the third quarter.
"I was really surprised that we didn't have the key player (Taumalolo), the guy that was actually making the easier yards through the middle that he didn't start earlier.
"And it showed, our third quarter was really average. To go into halftime at 6-8, under the pressure they were in the first quarter was outstanding.
"But it was really the second-half and the way they started, our back five were really pressured to get yards out of our own half and again the forwards didn't front-up."
Barnett was also critical of Johnson for failing to stamp his mark on the match and says the Kiwis made it easier for Australia by running set moves out the back rather than playing more direct and on the front foot.
"We all want him (Johnson) to be the player that can actually turn (a game) and dominate and dictate terms.
"He is such a talent, we know that, but at times he needs to dominate play, put his hand up and come out and shine.
"We didn't see him step, we didn't see him take the line on. We saw him try and get the ball on the outside but I'd rather him just go at the line and just step and just get on the front foot and play off the back of it.
"If we were guilty of anything, there were times when Taumalolo would run and dominate with a quick play the ball and we tended to play on the back with set pieces, which I hate.
"There were plenty of opportunities to play on the front foot."
Despite the demoralising nature of the five-tries-to-one defeat, Barnett is optimistic that the Kiwis will be able to improve when their Four Nations campaign begins against host's England on October 30 (NZT).
"There's a lot of improvements (left in the side), which is good, that's the positive and I believe that this side can turn things around quite quickly."