The Socceroos looked lethargic in the first half and had goalkeeper Mathew Ryan to thank for keeping the score level at halftime after some good saves to deny the hosts.
"First half was poor, we made a lot of mistakes, we ran too much with the ball. We weren't patient enough, also we had technical issues...," Marwijk said.
"OK, we did not concede and we (have) worked hard in the recent weeks - the players are tired.
"Second half was better and we took control. You saw, after 1-1 the team wanted to win. That is positive. Morally it was good, we won, but I already told my players, I wasn't satisfied."
Australia, heading to their fifth World Cup in Russia next week, raised their game in the second half and took the lead in fortuitous circumstances.
Daniel Arzani's fierce shot in the 74th minute caught goalkeeper Denes Dibusz by surprise, fumbling the ball as it went in.
However, Australia defender Trent Sainsbury headed into his own net after a misunderstanding with substitute goalie Brad Jones with two minutes remaining.
There was to be a late reprieve for the visitors as Tamas Kadar also scored an own goal in the 92nd minute to hand Australia a second victory ahead of their journey to Russia. Marwijk's side thrashed the Czech Republic 4-0 eight days ago in Austria.
Australia begin their World Cup campaign against Group C opponents France on June 16 in Kazan.
(The story corrects number of World Cup appearances for Australia from four to five in paragraph six.)
(Reported by Zoltan Fazekas; Editing by Christian Radnedge)
