Boyle, 33, fellow forward Brandon Borrello, defender Kye Rowles and goalkeeper Joe Gauci were the four players cut from the squad, announced on Monday AEST.
Scottish-born winger Boyle was selected for the Qatar 2022 World Cup but ruled out with a knee injury on the eve of the tournament.
This time, the forward missed out, likely as a consequence of Cristian Volpato's late defection from Italy and ultimate selection in the 26-man squad.
"Look, I'm not going to go into how he took the news. That's a private conversation that we had," Popovic said.
"But look, he knows he's played an important role in getting here."
Popovic pointed to Lucas Herrington, Awer Mabil, Tete Yengi and Volpato entering the selection fray late as proof the door was always open for new players - though that could be at the expense of stalwarts.
"So that's four players that had nothing to do with our campaign are now going to the World Cup," he said.
"So I've always kept the door open for everyone, and when you do that, it can cost someone that's been through the journey a spot at the World Cup, and unfortunately for Martin, he was one of those players."
Popovic said sitting down with the omitted players, as he had done with others earlier in training camp, had proved a difficult process.
"Those discussions are never easy, and there's no perfect way to give someone that type of news," Popovic said.
"Once they hear the news, how much they hear after that, I'm not sure really, in terms of whatever I say after that can be a blur to most of them.
"But they hear the news they don't want to hear, and that's the news that I have to give them.
"(They are) wonderful young men, professionals, have played a part in our journey in helping us qualify for the World Cup
"So it's tough for them, and they need to process that."
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