You can use doesntHave
and specify the boolean operator:
$products = Product::doesntHave('categories')->doesntHave('countries', 'or')->get();
Actually you only need whereDoesntHave
if you want to pass in a closure to filter the related models before checking if any of them exist. In case you want to do that you can pass the closure as third argument:
$products = Product::doesntHave('categories', 'or', function($q){
$q->where('active', false);
})->doesntHave('countries', 'or')->get();