Bergwijn, 26, signed for Al-Ittihad from Ajax for £17.7m on Monday.
The former Tottenham player has 35 caps after making his debut in 2018 including featuring twice at Euro 2024 as the Dutch reached the semi-finals before losing to England.
“The book is basically closed to him. He knows what I think about this,” Koeman said.
“When you are 26, your main ambition should be sporting, not financial. These are choices that players make.
“I have never been in that situation, because I could go to Barcelona. He could have stayed at Ajax, that’s not bad, is it? You have to respect that choice, but personally I wouldn’t (have moved).”
The Netherlands will play Bosnia and Herzegovina in Eindhoven, Netherlands on Saturday.
Memphis Depay has also not been selected, with the 30-year-old winger a free agent after leaving Atletico Madrid in June.
Koeman added: “It’s primarily because he doesn’t have a club. That means you don’t play football and you can’t be with the national team.
“Memphis is 30, let’s hope he gets a club and gets fit. Then he is still an option for me.”
Koeman also said it was unlikely midfielders Marten de Roon of Atalanta and Georginio Wijnaldum of Saudi side Al-Ettifaq will be selected in the future.
But he confirmed captain and Liverpool defender Virgil van Dijk, 33, had committed his future to the team until at least the end of the 2026 World Cup.
Koeman, who said he had flown to Liverpool for talks with Van Dijk, added: “I thought it was so important to go to him to see and feel with him. Are you going to give it your all for another two years at the highest level and do you still see a future for yourself? And he does. And I do the same with him. All doubt is gone, he just goes on.
“He admitted he did not reach the level you would expect from him as a player at the European Championship. As captain, I think he did a great job. But perhaps as a result, he put too much energy into others rather than into himself.”