Bryant's mother has said that she doesn't want authorities to pursue family violence charges against her son. Jones said he was taking the situation "very serious" but had not yet spoken to Bryant about what happened. The team owner said it was premature to discuss possible punishment since the team and the league were still gathering information.
Without getting specific about for what or how long, Jones said Bryant has been involved in the team's counseling program. Jones also pointed out that a lot of players take advantage of different kinds of counseling available.
"There is no doubt that Dez Bryant is exceptionally talented," Jones said. "It has certainly served to give him the consideration that's he's gotten frankly in life. And I think he, like us all, have got to realize where your bread is buttered.
"You've got to realize that that is not there for you if you do not adhere to society's rules. He's got to realize that."
Jones said Bryant and the team know controversy is not good overall for the Cowboys and is not good for the league, and that there are consequences.
"And we will deal with those as we move along and get more information," he said.
The Associated Press contributed to this report.