The Wallabies were thumped 54-34 last week by the All Blacks in the Rugby Championship opener in Sydney, but the scoreline only gained some respectability when they scored four tries after the world champions had established a 54-6 lead.
The result, coupled with a loss to Scotland and poor performance against Italy and Fiji in their June internationals, prompted an outcry from fans and former players.
Byrne, who was involved with the All Blacks for a decade as skills and then forward coach until after the 2015 World Cup, said it would take some time for the side to improve.
"If you go back, 2007 wasn't a flash year for us (the All Blacks), trying to get things right," Byrne told reporters in Christchurch ahead of their second Rugby Championship clash in Dunedin.
"But when it clicks into gear and you turn the corner, you turn it pretty quickly. The key is persevering with it."
The All Blacks were bundled out of the World Cup quarter-finals by France in 2007 and since then have dominated the sport, winning successive Webb Ellis trophies in 2011 and 2015.
World Cup winning Wallabies great Michael Lynagh had earlier led a chorus of criticism aimed at Australia.
"I can't overestimate how angry I am at seeing an Australian team have skills that are non-existent," former captain Michael Lynagh told Sky Sports in Britain.
"Passing and catching and making tackles and trusting the bloke beside you are pretty basic, even at schoolboy level."
Byrne, who returned to his native Australia after the last World Cup and then linked with the Wallabies last year, said he was already seeing improvements from the side.
"The improvements have been fantastic," he said. "It's been no different in any environment I've been in. You see the improvement on the training field before it transfers to the game.
"If we're not seeing it on the training field, that's when I get frustrated and that's when I start questioning what we're doing. It's just going to be persistence which starts the transfer on to the game.
"I understand people's frustration at not seeing it straight away. This is just hard work, it's going to take time."
(Reporting by Greg Stutchbury; Editing by Sudipto Ganguly)
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