In prepared, released statements, both Luck and Dana Holgorsen addressed the May 18 incident, but offered no information concerning possible punishments for the coach.
Luck, who returned to Morgantown early from Big East Conference meetings in Ponte Vedra, Fla., admitted that Holgorsen's behavior was not acceptable.
"After looking into the details and throughly investigating what took place last week, I believe inappropriate behavior did occur.
"Coach Stewart and I have made it clear, and will reiterate, that our coaches and staff are representing the University and the state at all times. We expect them to always display appropriate behavior.
"I take this matter very seriously, but I do not plan on commenting on it further."
Luck will handle any disciplinary actions internally, and will not make them public.
Holgorsen also released a brief, prepared statement.
"I learned a valuable lesson from this incident. As a football coach, I am always in the public eye and I have to hold myself to a higher standard, which is what I ask our players to do.
"I'm sorry that this incident has put the University and the football program in a difficult position. I will not put myself in that situation again."