Bergwijn, 26, completed a €21m (£17.7m) move from Ajax to the Saudi Pro League giants Al-Ittihad on Monday.
The winger was not selected for the Netherlands' upcoming Nations League fixtures against Bosnia and Herzegovina and Germany, amid the speculation surrounding his future.
In his press conference, Koeman slammed Bergwijn over the move saying it showed a lack of 'sporting ambition'.
In comments published by Dutch outlet De Telegraaf, a frustrated Bergwijn has bit back at Koeman insisting 'that's not how you treat your players'.
It comes after Koeman 'closed the book' on Bergwijn's international career, as he slammed the ex-Tottenham star for showing a lack of 'sporting ambition' by moving to Saudi Arabia
He said: 'I don't even want to play for this manager anymore. I won't play for someone who portrays me like he has done in the media.
'He could have called me, hear my side of the story. How can he say such things without talking to me?'
Bergwijn, has won 35 caps for the Netherlands and was part of Koeman's squad at Euro 2024 where they reached the semi-finals before losing to England.
And, speaking to the media on Tuesday after his group came together, Koeman hit out at Bergwijn when asked about the winger and claimed the move to Saudi Arabia has significantly impacted his international ambitions.
'Steven Bergwijn goes to Saudi Arabia at the age of 26,' he said. 'It's clear that this has nothing to do with sporting ambition.
Koeman was then questioned on whether Bergwijn had discussed the move with him, before he added: 'No, he probably knows what I would have said.'
The manager also said that the case was different to Georginio Wijnaldum who was still picked after he left Paris Saint-Germain for Al-Ettifaq last year.
He said: 'Georginio Wijnaldum once went that way because he had a problem at Paris Saint-Germain.
'He could only go to that country to play football until January. In Bergwijn's case is that he goes at the age of 26, sporting ambition does not prevail.'
Bergwijn played 60 times for Tottenham between 2020 and 2022 before joining Ajax.
At Al-Ittihad he will play alongside the likes of N'Golo Kante, Fabinho and Karim Benzema.