The Socceroos have twice reached the round of 16 but never gone further.
Popovic was adamant his charges could "do something special" and give Australia a reason to back them.
"I keep saying it to the group: one day, Australia will go very far in the World Cup. And why not this group?" he said.
"Why do we have to wait in two or three World Cups when I'm sitting back watching and applauding something special from the Socceroos? Why should we have limits? Why not do it now?
"We want to give ourselves every chance of doing that. I get a sense that the fans feel that as well."
Australia's national teams have long leaned into an underdog mentality but Popovic would rather put high expectations on himself and his players to compete with the best.
"We showed that against the US (a 2-1 loss) that we can compete," he said.
"But I want the players to also feel a bit disappointed they didn't get a result, as opposed to just walking off saying 'oh, we played good against the US. We competed well. Let's go home. We were expected to lose.'
"I want to be a part of something that we change the narrative. We expect a lot, and you guys expect a lot from the team, and expect a lot from me, and there's nothing wrong with that.
"If we do that, then I think the chances are that our young players, their mindset will be about playing at their best and winning for Australia, as opposed to 'I just want to play good for my country and just be competitive'.
"We know the World Cup is the hardest competition and we know that you can play well in three matches and not get through. But we also believe that we can do something special and maybe we can go further than we ever have before.
"And why not with this group? Because I know it will happen one day."
Popovic is overseeing Socceroos playing in Europe's top leagues, including ambitious talents like Jordan Bos, Nestory Irankunda and Mohamed Toure.
"Our football is growing within Australia and also the Australians are growing outside, and there will be names that we'll remember for a very long time, and there's some really talented young players coming through," he said.
"And I hope this group can feel the responsibility and feel the expectation and the belief that we can go out there and maybe be the ones that do something truly special."
Popovic is also open to bolters, be it from the A-League Men or elsewhere, making a late run at the squad.
"It's open. I envisage - maybe in March, I have a better idea - but I still feel from March to June, that someone can surprise us, that someone is in good form that is playing extremely well, that actually bypasses someone else," he said.
"And I don't want to put a limit or a stop on that and to announce in March that 'this is our squad, and there may be one or two more additions.'
"No, I want every player to feel that they have an opportunity."
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