Australia's Tim Cahill also praised his long-time international teammate.
"Mark Schwarzer a true professional and is one of the all-time greats for our game to ever wear a Socceroos jersey," Cahill said on Twitter.
Australia veteran Harry Kewell said he "didn't see it coming."
"I still believe he's our best keeper. He's playing at one of the best clubs in the world, so there's no reason why he should have done it but it's a personal decision and I'm sure all the players will respect it."
Former Australia striker John Aloisi said Schwarzer was "up there with the all-time great Socceroos players."
"What a great goalkeeper he was for the national team what a great career," said Aloisi. "We owe him a lot."
Schwarzer saved two penalties in a shootout against Uruguay which secured Australia's place at the 2006 World Cup the nation's first appearance in the event since 1974.
He began his career in Australia with Marconi from 1990 to 1994, then played in Europe with Dynamo Dresden (1994-95), Kaiserslautern (1995-96), Bradford City (1996-97), Middlesbrough (1997-2008) and Fulham (2008-13) before moving to Chelsea this season.
Schwarzer won a League Cup in 2003-04 with Middlesbrough and was named Fulham player of the year in 2008-09.
Schwarzer's international retirement leaves Mitch Langerak as the front-runner for the Australia goalkeeping role. He is the back-up keeper at Borussia Dortmund.
Langerak was included in Postecoglou's 22-man squad for the Costa Rica match.
Defenders Luke Wilkshire and Sasa Ognenovski were axed by the new coach and face an uncertain future with the side ahead of the World Cup.
Captain Lucas Neill was retained despite recent criticism of his leadership after the 6-0 losses to Brazil and later France that resulted in former coach Holger Osieck being fired. Postecoglou said Wednesday he would not guarantee Neill's continuing captaincy role past the Costa Rica match.