The result means that Korea Rep win the group on nine points followed by the Socceroos with six points, both qualifying for the quarter-finals.
The Socceroos found the going tough against a Korea Republic side far superior to Kuwait and Oman, who they easily beat in their earlier group games.
The Home side did have chances with six shots at goal compared to Korea's three.
The goal came in the 32nd minute when Ki Sung Yueng got past Ivan Franjic and sent a pass to Lee Keun Ho, who shot at goal from an angle.
His shot looked to be covered by goalkeeper Mat Ryan until Jeong-hyeop beat him to the ball to slide it into the net to make the score 1-0.
Four minutes later Australia almost equalised when James Troisi's shot hit the side netting.
Socceroos coach Postecoglou sent on Tim Cahill, Robbie Kruse and Mathew Leckie in the final 20-minutes to try and save the match and the move nearly paid off when Kruse came close in the dying minutes, with only the keeper to beat, was denied by a spectacular save from Kim Jin-hyeon.
Australia will remain in Brisbane for a quarter-final against China next Thursday.