Jesus Ramirez's header in the 38th minute proved the difference against an experimental Australian team at Shell Energy Stadium in Houston.
Few players, bar "fantastic" debutant goalkeeper Patrick Beach, impressed in an uncharacteristically flat performance.where Australia lacked drive, cohesion and potency and had just 34 per cent of possession.
In their second consecutive defeat, Australia also lost defender Jason Geria to a left hamstring injury in the 42nd minute.
It will give Popovic plenty to think about with just three more friendlies before picking his squad for next year's World Cup finals, starting with Wednesday's clash with world No.13 Colombia in New York.
"Great challenge on Tuesday (local time), and we know we have to be better, but that's part of what we're doing here and part of the process," Popovic said.
With Jordy Bos and Aziz Behich among a lengthy injury list, Popovic turned to Craig Goodwin at left wing-back.
The experiment didn't pay off, with Goodwin exposed for Venezuela's goal then hooked for Callum Elder at half-time.
Popovic otherwise fielded a relatively inexperienced team against a similarly understrength Venezuela, who missed World Cup qualification.
"There's a lot we have to assess, but in the end we lost, we're disappointed we lost the game," Popovic said, conceding Australia struggled physically.
"We gave a lot of players debuts, and we gave a lot of players an opportunity, some maybe in different positions.
"So it was a little bit difficult for us in that respect, and maybe players not quite understanding their roles - which is quite difficult in a couple of days - and making a debut et cetera.
"But we fought hard, we worked hard. We were probably a little bit too open.Â
"Venezuela technically were very good and were able to get into our box and obviously scored a goal, but it was a little bit too easy from our part."
Beach started ahead of Maty Ryan and Paul Izzo while Melbourne City defender Kai Trewin and Sydney FC midfielder Paul Okon-Engstker, son of Socceroos assistant Paul Okon, also started on debut.
Al Hassan Toure was the fourth debutant in the 78th minute, after brother Mohamed had already been substituted, becoming Popovic's 12th debutant in 13 games.
Mohamed Toure spurned two great chances in the opening six minutes, before Venezuela got on top.
Beach made an extraordinary reflex save to bat away Jesus Ramirez's goal-bound header in the 17th minute.
For the goal, Goodwin was caught high up the pitch and Ender Echenique was released down the right wing, cut inside Trewin then squared the ball for Ramirez to tap home.
"Really, it's a soft goal for us to give away," Popovic said.
"But maybe the contribution of that is having a debutant at left centre-back, Craig Goodwin at left wing-back.
"... But okay, it was a lot of learnings for us, and we move on."
A minute into the second half, Beach denied Ramirez with a diving save.
Riley McGree and Jackson Irvine returned from injury in the second half and the substitutes lifted Australia.
Al Hassan Toure forced an excellent Contreras one-handed save in the 86th minute, but it proved too little too late.