And once they join a Socceroos camp, they should be all-in on a team Degenek is adamant will only get bigger and better.
The Socceroos have had mixed results when it comes to players of dual-eligibility picking their nation of choice.
Alessandro Circati chose Australia over Italy and Harry Souttar picked the Socceroos over Scotland, but Nectar Triantis recently switched eligibility to Greece.
Alexander Robertson (England, Peru, Scotland) recently declared for the Socceroos as did James Overy (Scotland), but Cristian Volpato previously rejected Graham Arnold's overtures to try and play for Italy.
Coach Tony Popovic has made it clear he won't "beg" players to represent Australia.
Degenek, of Serbian descent, played for Australia and Serbia at youth level before making a "very simple" decision to commit to the Socceroos.
"I looked at what country gave me, my family and my loved ones the best opportunity to live a normal, healthy life," he said ahead of Saturday's friendly against Venezuela in Houston.
"Coming from a war-torn country, surviving through two wars and then coming to Australia was an eye-opener for us.
"And I've said this many times ... but I can't give back to Australia what they've given to me and my family, but I try and repay that with the utmost respect that I can on the pitch."
Degenek said players' decisions needed to come from within.
"It can't be someone telling you, 'oh, please play for us'. You have to have that feeling yourself," he said.
"And if you're not content with what you feel inside to come play for Australia, then you shouldn't be here.
"Once you come here, you have to be 110 per cent behind that feeling and play for this country with pride and joy and love.
"The boys that are on the fence, I think they need to realise what this country offers you and what this football country offers you and what the Socceroos offer you and to realise that the Socceroos are actually one big family.
"It's not just a national team where you're just a number. It's a national team where we're a part of a big family and it's a national team that's going forward and I believe going forward it's going to be even bigger and better."
Last month, Popovic hailed Degenek as a surprise success story as he had never expected to call upon him given his 18-month injury battle.
"It was really special that he said something like that, nice about me, it means a lot to me, and it speaks highly of him as the person he is," Degenek said.
"For me, it's just shown that he's given me a little bit of trust, and I've tried to repay that as best I could when I play, and I'll continue to try and repay that when I play and when I'm in camp."
13°C