B767 Captain reported uncommanded aircraft movement during push back not noticed by flight crew until advised by ground crew. Captain set the parking brake to stop aircraft movement.

Narrative

The following is to report unintended aircraft movement during push back. I was the Captain conducting First Officer (FO) new hire and had a new hire occupying the observer seat for familiarization. Work load management was high and leading factors include; fatigue; 2nd leg of an all-night duty period; MEL procedures; and training environment. During push back the ground crew completed the push advised me to set the parking brake and we are cleared to start both engines. I set the parking brake and told the FO to start the right engine. During the start the observing crew member asked if I could explain the start process; to which I only explained our definition of max motoring prior to fuel selection. Also; my attention was focused outside of the aircraft and compliance with verification of proper mode annunciation by EICAS and discrete light. After the right engine was started normally; the ground crew advised the aircraft was rolling and to set the parking brake. I immediately stepped on the brakes; set the parking brake and verified EICAS that the brake was set.I verified with ground crew if there were any injuries; contact with equipment or any damage. The ground crew was all safe and uninjured; no damage or contact with equipment took place. The aircraft was pushed to a dark unlit area on blacktop; it is unsure how much speed the aircraft picked up; but was not enough to make contact with the tug or tow bar parked directly in front. After the aircraft was briefly inspected by local maintenance; the left engine was started and we completed the flight without further issue. My apologies were given to the ground and well done for advising of the aircraft movement. I sincerely apologize to the company and to the crew members aboard for the potential harm or damage that could have resulted. Please contact me with further questions.