Popovic sparked criticism from some high-profile former Australia players for substituting first-choice goalkeeper Patrick Beach deep into extra-time in the last-32 clash in Dallas on Friday as penalties loomed.
He instead turned to Mathew Ryan, who failed to pull off a save and Egypt won 4-2 on spot-kicks.
The result left Australia still searching for a first victory in the knockout stages of a World Cup.
Popovic also came under scrutiny for entrusting 18-year-old Lucas Herrington with one of the penalties, which he missed.
“Every fan will think about what can be done better,” Football Australia chief executive Martin Kugeler told Australian media in Dallas.
“But the coaching staff and Tony Popovic are always in the best place to judge in that moment what is needed for the team.
“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.”
Popovic was appointed in 2024 and guided Australia to their sixth successive World Cup.
His contract was extended in the days before the tournament through to the 2027 Asian Cup which is due to be held in Saudi Arabia from January 7 to February 5.
“We’re absolutely happy about the decision to extend this contract,” Kugeler said.
“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.”
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