Koeman said he will not select Bergwijn after the 26-year-old forward made a £17.7m move from Ajax to Saudi Pro League club Al-Ittihad on Monday.
The former Everton and Southampton boss believes the move shows Bergwijn’s main ambition is financial, not sporting, and added “the book is basically closed to him.
“He knows what I think about this.”
However, the ex-Tottenham forward says he has not spoken to Koeman about his move to Saudi Arabia.
“I don’t even want to play under Koeman anymore,” Bergwijn told Dutch newspaper De Telegraaf.
“I won’t play for someone who portrays me like he has done in the media. He could have called me, heard my side of the story. How can he say such things without talking to me?
“If he had been a committed national coach, he would have called me first. Now I had to hear about it on TV. I’ve had many beautiful moments with him, so this is far too easy and I’m disappointed with him.”
Asked about the comments on Friday, Koeman said it is “logical” that Bergwijn would react but they “will not discuss it further”.
He added: “It does not affect me at all. I only said that this step does not show sporting ambition. I did not say much more.”
Koeman gave Bergwijn his international debut in 2018, during his first spell as Netherlands coach, and the PSV Eindhoven academy product now has eight goals from 35 international appearances.
After a brief stint in charge of his former club Barcelona, Koeman returned to the Dutch job last year, during which he criticised Ajax striker Brian Brobbey’s technical ability.
“He had previously publicly expressed an opinion about Brobbey, which was also not nice and which he later said was not smart,” Bergwijn added.
“That is not how you treat your own players. If he continues like this, he will lose all his credibility.”