The video emerged just hours after the 'Mackems' lost 5-0 to Celtic in their final game of pre-season.
The statement read: "Darren Gibson has not conducted himself in a manner befitting Sunderland Football Club.
"As a consequence, we will initiate our internal disciplinary process to deal with the matter. Darron has apologised this morning."
Gibson has played 12 times for the Wearsiders since joining the club from Everton in January.
The Repbulic of Ireland international was filmed saying "we're f***ing s**t" before questioning the commitment of several of his team-mates.