According to the KSA, a number of unlicensed online gambling providers shut down their websites quickly or block Dutch customers when confronted with legal action from the regulator.
The KSA requires all gambling sites without a licence to block Dutch customers, rather than simply avoiding targeting the Netherlands.
Entain, Kindred, 888, Betsson and LeoVegas were among the operators that agreed to block all Dutch customers until they became eligible for licences.
However, this could mean that players may not be able to access their funds and will lose money.
The regulator added that there was no guarantee of a refund from a site that is inaccessible from the Netherlands.
The regulator reminded customers that gambling online with licensed operators has been legal in the Netherlands since 1 October, when the market opened.
The KSA also provided an update on the 25 illegal gambling websites it had chosen for investigation in November. This was launched to ensure Dutch customers were blocked from the selected sites.
The regulator said that it had since added more websites to the investigation and will contact the relevant parties in due course.
Earlier this month René Jansen, chairman of the KSA, warned licensees to limit advertising to avoid a clampdown from the regulator.