Australia wanted a response from Saturday's flat 1-0 loss to Venezuela and turned in a vastly improved performance, until Colombia skipper James Rodriguez converted a contentious penalty in the 76th minute.
Superstar Luis Diaz added a second goal from a defensive mix-up in the 89th minute before Jefferson Lerma bundled home four minutes later at New York's Citi Field.
It was a particularly disappointing end given a a back five marshalled by Milos Degenek had defended with aplomb for the first 75 minutes.
Popovic lamented what he termed the "softest penalty you can see", also revealing the entire squad had been bedridden with a virus and been unable to train on Sunday ahead of the game on Tuesday (local time).
"We kept that quiet, because the players wanted to keep that quiet. So that's a credit to them," he said.
"I was happy to mention that, but the players wanted to keep that quiet. We had a virus through the whole squad, including the staff, so we were unable to train Sunday. So the entire day, everyone was in bed.
"We flew three hours on Monday, came here and put up a really good, brave performance.
"I'm actually surprised at how well they did, because physically, they were clearly nowhere near it."
It was the Socceroos' final game before the World Cup draw on December 5, while they won't be in action again until the March window.
Australia's pot for the draw is yet to be confirmed.
The Socceroos have never beaten Colombia, who had 16 shots (eight on target) to two (one), in five attempts.
Australia have now won just nine of 50 matches against South American opposition.
Popovic made five changes, including the starting returns of Jackson Irvine and Riley McGree and Australia showed far more intent to retain possession than they had against Venezuela.
But the Socceroos still lacked precision going into attack as Colombia's defence expertly isolated young striker Mohamed Toure.
"We've just got to get better when we get in that front third, that we can turn that good play into a good chance on goal," Popovic said.
Colombia took the lead from the spot after referee Tori Penso ruled Callum Elder had fouled Santiago Arias, and Rodriguez dutifully sent Paul Izzo, selected ahead of Maty Ryan, the wrong way.
"It's never a penalty. It's the softest penalty you can see. I'm sure we don't get that tonight," Popovic said.
"It's unfortunate to say that, but I'm sure it's true. Without VAR, that's such a soft penalty to give.
"... After that, it's more difficult for the players, and we gave away two soft goals at the end. Which is a shame for the players, because I thought they acquitted themselves very well.
"...It's just unfortunate it blew out at the end, because it's certainly not what we deserved."
Defender Milos Degenek said to Paramount Plus: "No excuses, but the ref just kills the game.
"... We asked for an explanation, she has absolutely no idea what she's done.
"So she's killed the game there and it's just gone pear-shaped from there."
Popovic responded with a triple change, calling upon Nestory Irankunda, Martin Boyle and Paul Okon-Engstler to chase the game.
But Australia were unable to manufacture an equaliser and two defensive lapses proved costly.
The Socceroos defence got caught out by a long ball over the top and Izzo came off his line to try to defend Rafael Santos Borre, but it spilled to Diaz to tap home.
Then, Izzo saved Lerma's initial header from a set piece but the defender recovered to bundle home a third.
15°C