Eales, who shared in Australia's World Cup wins of 1991 and 1999 said ranking behind rugby league, Australian rules, cricket and soccer in popularity, rugby needs to bounce back hard from its World Cup disappointment or risk falling further in public eyes.
Eales told The Rugby Paper, "You're always competing for the hearts and minds of people and it's easier to do that when you're winning.
"There's no question of that. When the Wallabies have gone through their successful eras, they've been right in the centre of the thoughts of the sporting world in Australia.
"It is harder when you're not getting the regular wins," he said.
Knocked out of the Cup quarterfinals by eventual beaten finalists England, Australia had failed to build on their record win over the All Blacks in Perth to open the Investec Rugby Championship season.
Coach Michael Cheika had stepped down but Eales believes all is not lost.
"I think the people who have been watching it will have seen our schoolboys team have a very good year, our Under-20s team had a very good year at the World Cup, although not quite winning it.
"So there is that good talent coming through. While there have definitely been some challenges in Australia, there's also a great will to see the team succeed.
"Hopefully this next generation of players, who are getting some success at a younger age, can come through and experience it at the next level," he said.
"The players want a coach who can deliver a successful environment which will allow them to improve and grow," Eales said.
While former Chiefs coach, now coaching Glasgow, Dave Rennie was frontrunner in favouritism to take on the coaching role, Eales noted the success Rennie had enjoyed but added a lot of other candidates had also been very successful.