Coming into the clash against the World Cup co-hosts, Australia were riding a seven-match winning streak - undefeated in their last 12 games and 11 since Popovic took over from Graham Arnold over a year ago.
Another win beckoned at Dick's Sporting Goods Park when wingback Jordan Bos netted early, but the visitors were overhauled 2-1 by the world number 16 Americans after a brace from striker Haji Wright.
"I think we showed tonight that we can definitely be competitive at the World Cup," Popovic told reporters.
"I thought we competed against a very good team, very well, throughout the game.
"We pressed very high early, we had some good opportunities at 1-1.
"We did not get the win but I thought we had a good performance, a better one than what we had against Canada (when) we got the win."
World number 25 Australia, who qualified mid-year for the 2026 World Cup in North America, have previously struggled to score, but they have added new dimensions to their attack with the development of 19-year-old Nestory Irankunda and 21-year-old Mohamed Toure.
Irankunda scored the winner in a 1-0 friendly against World Cup co-hosts Canada in Montreal last week, but started on the bench with Toure on Tuesday.
Introduced after the hour mark, Irankunda conjured a good chance late on with a barrelling run into the box, but was unable to produce the equaliser Popovic sought.
The coach said the younger players laboured in the thin air at a venue 5,200 feet (1,584m) above sea level, the highest elevation among Major League Soccer stadiums in the US.
"You could see they were struggling to breathe and they couldn't repeat the efforts (of) the senior players .... who handled that well," said Popovic.
"So they showed a glimpse of their quality, but I thought we lost a little bit of momentum when they came on."