The Roar trailed by a goal up until the 65th minute, when Kosta Barbarouses canceled out Gerald Sibon's opener, before Costa Rican striker Jean Carlos Solorzano grabbed a late winner from close range.
Although Postecoglou admits his side may have been lucky to not fall behind further after Heart's goal, he was full of praise for his charges after they completed a tough fightback.
"We were very flat in that first half and to their credit they started stronger and really came at us," Postecoglou said.
"We sat back which is very unlike us and were probably lucky to get away with being one nil down at half time.
"In the first half I don't think we had too many winners.
"The whole team stepped up in the second half and we played more like ourselves."
"Ivan and Mitch were good when they came on and they changed the game for us," he added.
"But as I said, I thought the whole team stepped up and we deserved the win in the end with the chances we created."