The quarry was on private land.
While it is not known how the youths entered the private property, preliminary investigations show there were numerous potential access points, including an open gate.
Two of the youths received minor injuries in the incident while a third suffered severe abdominal injuries after being pinned under the vehicle.
The regulator said all mines and quarries must have adequate site security and where gates were required, they must be used and secured to prevent unauthorised access.
The incident is the subject of an ongoing investigation.