Rogic played the first half in the hit-out against the lowly division two side but was replaced by James Troisi after a performance that lacked intensity as the playmaker appeared sluggish.
On the other hand, midfielders Oliver Bozanic, Massimo Luongo and Ben Halloran put in strong showings in hope of being named in Postecoglou's final 23-man squad.
Rogic emerged from a tackle in the 10th minute walking slightly gingerly for a moment, which may have affected him.
But fears about his lack of game time and whether his body can withstand the rigours of a full 90 minutes appear to be justified.
No-one expected an explosive performance as Postecoglou has been putting his charges through rigorous bootcamp-like training.
And just like in the farewell game against South Africa, the Socceroos faded after looking dynamic and energetic in the first half.
Bozanic looked strong in the holding midfield role alongside Luongo, putting Australia in front in the 18th minute off a Dario Vidosic cross.
Halloran, playing on the right wing, exhibited pace as both he and Bozanic backed up their strong showings against South Africa when they looked dangerous as second-half substitutes.
Adam Taggart doubled the advantage in the 28th minute after Luke Wilkshire set him up, and the Newcastle Jets frontman could provide another option at the point of attack should Josh Kennedy's back complaint persist.
Troisi could have made it 3-0 in the 78th minute but misfired from point-blank range.
Postecoglou made a further two substitutes, bringing James Holland on for Vidosic late in the second half and giving goalkeeper Mark Birighitti the final few minutes between the sticks in place of Eugene Galekovic, who was barely troubled.
Socceroos line-up: Galekovic, Wilkshire (c), McGowan, Wright, McKay, Bozanic, Luongo, Vidosic (Holland), Halloran, Rogic (Troisi), Taggart.
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