Pochettino's side had impressed for large parts of the tournament, topping their group and beating Bosnia and Herzegovina in the Round of 32, but were comprehensively outplayed in the last 16 by a Belgium team inspired by Charles de Ketelaere's double, a Hans Vanaken strike and a late Romelu Lukaku finish.
Malik Tillman's free-kick had briefly levelled the contest, but the USA rarely threatened beyond that. Christian Pulisic cut a frustrated figure before a leg problem forced him off, and Florian Balogun barely got a sight of goal despite FIFA's contentious late move to lift the suspension that would otherwise have ruled him out.
Speaking to talkSPORT, Lalas stopped short of calling for an immediate departure but was unequivocal that the Belgium result should mark the end of Pochettino's tenure.
"I mean, it's not that I want him to leave," the 56-year-old said. "I just think that this cycle has run its course."
Lalas argued that a narrow defeat to Spain in the quarter-finals, the fate that ultimately befell Belgium, would have been a more forgivable outcome than the manner of the Round of 16 exit.
"When it comes to Mauricio Pochettino, you had one job," he said. "And it was the game against Belgium. You win that game, then you're in some rarefied air. And it's not gravy but let's be honest, you're playing against Spain. And you take your chances, you're back in an underdog type of role.
"So I think that they [US Soccer] move on. I believe he's had a good time, but you had one job, and you blew it. And, you know, you live and die by that. Every coach understands that, every manager understands that, and certainly Mauricio Pochettino does."
Lalas was equally scathing about the nature of the collapse rather than simply the result itself.
"It was an abject failure," he said. "It's one thing to go out to Belgium, it's another thing to go out in the way they went out, especially with the way that they looked through the tournament. I don't think the confidence and excitement was misplaced for this team, but they picked the worst possible day to play their worst possible game. It's obviously on Mauricio Pochettino and these players.
"Does it completely negate everything they did? No. But the reality is a lot of that goodwill and a lot of the people that came into the tent... they're left shaking their head and there's an inquiry going on right now... rightfully holding this team and this coach to account."
The comments add to mounting scrutiny of Pochettino's position after a tournament that began with genuine optimism but ended in a familiar last-16 exit, a stage the USA has been unable to progress beyond since reaching the quarter-finals in 2002.