The Roar grabbed top spot on the A-League table with their 4-1 win, becoming the first team to beat the Phoenix at Westpac Stadium in 25 games.
"The boys were fantastic tonight, absolutely brilliant," Postecoglou said.
"We started really well and I thought we were always threatening going forward.
"We defended really well as a unit and even after conceding the goal the boys didn't drop their heads and we looked solid.
"After scoring the second goal before half-time, I thought we came out in the second half and tore them apart."
The Phoenix did come at the Roar hard when the score was 2-1 but the visitors managed to keep their cool and work right until the final whistle.
"We really kept our composure towards the end of the match," Postecoglou added.
"The substitutes came on and made a massive impact.
"Both Nichols and Solorzano came on and worked hard for the side and that's what you want out of your substitutions.
"The boys felt really good before the game, even though we'd played on the weekend and were really looking forward to the game.
"I think you could see that out there."