The US, which won the quarter-final 4-2 on aggregate thanks to a 3-0 victory in Austin last week, earned a spot in the 2024 Copa America despite the loss in Trinidad.
Dest assisted Antonee Robinson's opening goal before being sent off in the 39th minute. He received the first yellow for kicking the ball off the pitch and the second for showing dissent as his teammates tried to calm him down.
Trinidad levelled minutes later, with Alvin Jones giving them the lead in the 57th minute.
"It is concerning because that's not what we want to represent," Berhalter told reporters. "As a team, players, the staff, we need to hold him accountable because it's inexcusable.
"It really is and we were very firm with our words after the game. He put a number of guys in jeopardy and made a number of guys do a lot of extra work in this weather and it's inexcusable."
Berhalter said he does not want this situation to become a "witch hunt" and that Dest had apologised to the team.
"He's a young player, he's a fantastic part of this team. He's going to learn, he's going to grow. He made a dumb mistake and he knows that," Berhalter said.
Dest also apologised on Instagram, saying his behaviour was "unacceptable, selfish and immature".
"It's something I have to learn from and it won't happen again!," Dest said.
