Reyna's comments came after Berhalter's weekend remarks that the team had a player "clearly not meeting expectations on and off the field" whom they had contemplated sending home, according to the Charterworks newsletter.
While Berhalter did not name him, several news outlets identified the player as Reyna.
"Just before the World Cup, Coach Berhalter told me that my role at the tournament would be very limited. I was devastated," Reyna said in an Instagram post.
"I fully expected and desperately wanted to contribute to the play of a talented group as we tried to make a statement at the World Cup.
"I am also a very emotional person, and I fully acknowledge that I let my emotions get the best of me and affect my training and behavior for a few days after learning about my limited role.
"I apologised to my teammates and coach for this, and I was told I was forgiven. Thereafter, I shook off my disappointment and gave everything I had on and off the field."
Reyna did not start in any of the team's four games but played the entire second half in their Round of 16 loss to the Netherlands.
Many US fans were perplexed by the Borussia Dortmund standout's lack of playing time during the tournament given the team's struggle to score goals.
Berhalter told the ESPN network that his remarks to a leadership conference in New York were supposed to be off the record. US Soccer did not immediately respond to a request for comment.
Reyna said he took issue with the situation being made public.
"I am disappointed that there is continuing coverage of this matter (as well as some highly fictionalised versions of events) and extremely surprised that anyone on the U.S. men's team staff would contribute to it," he said.
"Coach Berhalter has always said that issues that arise with the team will stay 'in house' so we can focus on team unity and progress," he added.
"I love my team, I love representing my country, and I am focusing now only on improving and growing as a soccer player and a person."
