Switzerland draw shows Socceroos can 'punch above their weight', says Popovic
Dan Ndoye gave the Swiss the lead in the 14th minute in San Diego, but debutant Tete Yengi equalised for Australia in the second half.
This match was the last warm-up for both teams before the World Cup, which starts on Thursday.
Popovic selected an experimental starting XI, making seven changes from the side that lost 1-0 to Mexico last week, before switching to a probable first-choice team for the second half.
"I am just pleased. We have no injuries and we have come through the game," Popovic said.
"We need to start better next week, of course, and that will help us."
Australia, appearing at their sixth consecutive World Cup, are in Group D alongside Turkey, co-hosts the United States and Paraguay.
The Swiss are drawn with Qatar, Bosnia-Herzegovina and co-hosts Canada in Group B.
Popovic said he was encouraged by the draw against a near full-strength Swiss team ranked eight places higher than Australia in 19th place, and believes his young side can progress to the knockout stages.
"If you ask any Australian, they anticipate being there at the very end because we always feel we can punch above our weight," he said.
"We have proven that repeatedly in every sport, and we have done it in football. So we have demonstrated our capabilities."
Four years ago in Qatar, Australia advanced from the group stage and pushed eventual champions Argentina close in the round of 16, eventually losing a brave 2-1 contest masterminded by Lionel Messi.
"We want to progress, and that is the challenge we face," added Popovic.
"We want it to be a knockout phase where we know anything can happen.
"But if we break it down, there is a lot of work to do before then, and we have a very tough group, but I would like to think that our opponents will also view us as a difficult challenge."
Australia begin their World Cup campaign against Turkey in Vancouver on 13 June, while the Swiss start against Qatar in San Francisco on the same day.