The 29-year-old - a January signing from Everton - was secretly filmed by a fan in a bar last weekend describing the Black Cats as "fucking shit" and accusing some of his teammates of "not giving a fuck".
Gibson's comments came after the club - relegated from the Premier League last term - were humiliated by Scottish champions Celtic in a 5-0 friendly loss at the Stadium of Light.
"I think it's been acknowledged that it wasn't a very good thing to do," Grayson is quoted as saying by The Sun. "The club have dealt with it internally. We've decided on the plan of action and that's to deal with it internally.
"Players should be more responsible in this day and age. Social media plays a massive part in football – people are there to wind people up and make you say things you shouldn't say.
"Darron Gibson has admitted it and apologised that he was bang out of order. It has been dealt with. It is something that we didn't need leading up to the start of the season. Unfortunately, it happened and we dealt with it and we can look forward to the start of the season now."
Sunderland begin the Championship season with a home fixture against Derby County tomorrow night.