FA extended Popovic's contract until after next year's Asian Cup before a ball was even kicked at the World Cup.
Australia suffered a heartbreaking 4-2 loss to Egypt on penalties in the round of 32, with scores locked at 1-1 after regular and extra time.
Popovic has come under scrutiny for his unsuccessful decision to substitute in-form goalkeeper Patrick Beach for skipper Maty Ryan - who hadn't played a minute all tournament - for the penalty shootout.
FA chief executive Martin Kugeler and football director Heather Garriock had no qualms with the goalkeeper switch, nor the call to list 18-year-old Lucas Herrington - who missed his spot-kick - fourth in the penalty takers.
"Every fan will think about what can be done better, but the coaching staff and Tony Popovic are always in the best place to judge in that moment what is needed for the team," Kugeler said.
"In hindsight, everyone always knows better, but you have to make those calls in the moment based on what you've seen in training, what is your impression in talking to the players.
"So Tony Popovic has absolutely our confidence."
Garriock said she had "full belief" in Popovic, who she described as a brave and methodical coach, and wasn't surprised by the Ryan-Beach switch.
When asked if he was comfortable with the early call on Popovic's contract, Kugeler said: "absolutely".
"Just wind back to the time when Tony Popovic took over, we were in a difficult spot for the World Cup qualification," he said.
"He took us to direct qualification, a winning streak of 11 games, building depth of the squad - and then let's look at this World Cup."
Kugeler hailed Australia's unexpected 2-0 victory over Turkey, their second half against the US and a mature performance against Paraguay.
"So getting out of a very difficult group and qualifying for the round of 32 has been an enormous success," Kugeler said.
"So, yes, we're absolutely happy about the decision to extend this contract.
"He is the right person to now take this group into the next major tournament and apply all the experiences, all the learnings from this tournament into the next major tournament."
The Socceroos again fell short of an elusive knockout win at the World Cup and didn't score - bar an Egypt own goal - in their final three games.
When asked if FA was satisfied, Garriock said: "We certainly are satisfied with the result, but there's always more left in us."
13°C