"That's a decision we'll make during camp. It's not the highest on my priority list right now," he told SBS World News Australia.
"More importamtly is to get all the players in. Obviously we're starting on a new journey with my first camp and the priority for me is to get the players some relief from the way we want to play.
"Let's see who fits into that and once we announce the team, we'll slot in the captain as well."
Postecoglou says the retirement of Mark Schwarzer did come as a surprise.
"It certainly came as a surprise. He was named in the squad and for all intents and purposes we expected him to be here.
"All I can do is respect his decision."
He says he will be taking the same philosophy he used as the coach of the Brisbane Roar and Melbourne Victory in his new role as the coach for the national team.
"I like to play a possession-based game and I like to play attacking football," he said.
"And there will be minor adjustments because of the international spectre of what we do, but the basic philosophy of what we do will be there."
The axing of Australia defenders Luke Wilkshire and Sasa Ognenovski, and the retirement of Mark Schwarzer, has sent warnings to an ageing core in the first Socceroos squad picked by new national head coach Ange Postecoglou.
Schwarzer, Australia's most-capped player, quit international football hours before Postecoglou announced a 22-man squad for a friendly against Costa Rica on 19 November in Sydney.
Schwarzer was set to be included in the squad but decided to end his decorated 109-game international career, leaving 25-year-old Mitch Langerak as frontrunner for the goalkeeping role.
But Wilkshire, 32, and Ognenovski, 34, face an uncertain future after being snubbed by Postecoglou.
Captain Lucas Neill was retained, along with fellow stalwart Mark Bresciano, as Postecoglou took a measured first step on the path to regenerating the Socceroos.
But all face pressure to extend their international careers to next year's World Cup in Brazil, with Neill battling to keep the captaincy from likely replacement Tim Cahill.
Postecoglou selected a squad with a notable A-League flavour by picking Ivan Franjic (Brisbane Roar), Matt McKay (Roar), Mark Milligan (Melbourne Victory) and Michael Zullo (Adelaide United).
"I'm excited by the squad we have named," Postecoglou said.
"The first task is to have a good look at the bulk of the players who played a significant part in qualifying Australia for the 2014 World Cup and also giving opportunities to players I think have the ability to improve the team.
"I want to give every Australian player the best opportunity to stake a claim for Brazil and beyond."
Ryan McGowan returns to the Socceroos squad after missing the previous matches against France and Canada as does Tom Rogic, who was ruled out of last month’s matches because of injury.
Postecoglou was appointed on an unprecedented five-year contract after German-born coach Holger Osieck was sacked last month after consecutive 6-0 away defeats to Brazil and France.
This will be the first international match between Australia and Costa Rica at senior men’s international level.
Costa Rica, which is currently ranked 31 in the FIFA World Rankings, has also qualified for the 2014 FIFA World Cup after finishing in second place of the CONCACAF qualifiers.
Australia squad to face Costa Rica on 19 November, Allianz Stadium, Sydney
Oliver BOZANIC
Mark BRESCIANO
Tim CAHILL
Jason DAVIDSON
Ivan FRANJIC
James HOLLAND
Mile JEDINAK
Josh KENNEDY
Robbie KRUSE
Mitchell LANGERAK (gk)
Matthew LECKIE
Ryan McGOWAN
Matthew McKAY
Mark MILLIGAN
Lucas NEILL
Tommy OAR
Tom ROGIC
Mat RYAN (gk)
Dario VIDOSIC
Rhys WILLIAMS
Alex WILKINSON
Michael ZULLO
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