The National Football League's culture is broken, Houston Texans owner Robert McNair told CNBC on Wednesday, with the league grappling to manage the fallout from two high-profile domestic abuse cases.
With two marquee running backs caught in a whirlwind of domestic abuse charges, NFL Commissioner Roger Goodell is facing criticism and calls for his resignation. However, McNair told "Squawk Box" that he stands 100 percent behind Goodell in his capacity to run the league.
The NFL's issues are a microcosm of society's own problems, McNair said. Still, athletes are role models— whether they want to be or not, he added.
"We just have to recognize that we are bing held to a higher standard and we need to act to a higher standard," the team owner said. "What we have to say is 'zero tolerance', and we're not going to put up with it."
The NFL needs to say it's not going to tolerate domestic violence, McNair told CNBC. And going forward, he said teams can refuse to draft players who were involved in legal issues.
His comments came after the Minnesota Vikings reversed course and announced early Wednesday that Adrian Peterson has been barred indefinitely from all team activities. The running back faces charges of hitting his 4-year-old son with a stick as a form of discipline.
"After giving the situation additional thought, we have decided this is the appropriate course of action for the organization and for Adrian," the team said in a prepared statement on Wednesday. "We will support Adrian during this legal and personal process, but we firmly believe and realize this is the right decision. We hope that all of our fans can respect the process that we have gone through to reach this final decision," they added.
Pepsi, also a mainstay of NFL advertising dollars, said on Wednesday that it was "encouraged to see the NFL is now treating this with the seriousness it deserves," calling domestic violence "completely unacceptable."
The Vikings' reversal came after the Radisson hotel chain suspended its sponsorship with the Vikings, while Nike also put its contract with Peterson on ice. Papa John's pizza was considered doing the same. Meanwhile, Castrol Motor Oil, Special Olympics Minnesota, and Mylan all severed ties with Peterson, and Twin Cities Nike stores pulled Peterson's jerseys from its shelves.
The Vikings are now addressing the Peterson situation properly, McNair said on Wednesday.
Teams need to take individual responsibility for these issues, but are limited in how much discipline they can exert on the players, he added.The Vikings had initially said Peterson could play while the legal process played out.
Separately, the NFL players union on Tuesday night appealed the indefinite suspension imposed on Ray Rice by the league earlier this month. The Baltimore Ravens released the running back on Sept. 8 after video emerged of him punching his then-fiancee in an Atlantic City, New Jersey, casino elevator in February. Rice had originally been given a two-game suspension in July under the NFL's personal conduct policy.
Sponsors including Anheuser-Busch, the second largest in the NFL, are expressing concern about the league's response to Rice and Peterson cases.
"We are not yet satisfied with the league's handling of behaviors that so clearly go against our own company culture and moral code. We have shared our concerns and expectations with the league," the NFL's official beer sponsor said in a statement.
Read MoreAnheuser-Busch lashes out at NFL over incidents
Other companies such as FedEx, General Motors and Marriott have all released statements saying they're monitoring the situation.
In response, the NFL said, "We understand. We are taking action and there will be much more to come."
Meanwhile, Sen. Cory Booker, D-New Jersey, introduced legislation Tuesday to close a decades-old tax loophole used by professional sporting leagues, including the NFL. Under current law, individual sports teams pay taxes but the dues each team pays to support the front offices of the leagues are not taxed.
—By CNBC's Matthew J. Belvedere and Javier E. David. The Associated Press contributed to this report.