"These are serious violations and we understand the negative impact it has had on our game," Payton and Loomis added. "Both of us have made it clear within our organization that this will never happen again, and make that same promise to the NFL and most importantly to all of our fans," Payton and Loomis said in a joint statement Tuesday.
Payton and Loomis also said New Orleans owner Tom Benson "had nothing to do" with the bounty pool.
"We acknowledge that the violations disclosed by the NFL during their investigation of our club happened under our watch. We take full responsibility," they said.
The league's investigation, released last Friday, said the bounty program was funded primarily by players for the past three seasons and was overseen by former Saints defensive co-ordinator Gregg Williams. He admitted to running the program and apologized within hours after the report surfaced.
The NFL said it confirmed Benson was unaware of the program, and that he told Loomis to stop it immediately, but that Loomis did not. The league also said Payton, though not directly involved, was aware of the bounty pool, but did nothing to stop it.
Williams now is defensive co-ordinator for the St. Louis Rams. He met with NFL security officials on Monday as part of the league's ongoing investigation.
Once it concludes — the league says there is no timetable — Roger Goodell likely will hand out the stiffest penalties of his 5 1/2 years as commissioner.
Goodell has frequently taken a hard line on any action that threatens player safety. He suspended Detroit's Ndamukong Suh for two games for stomping on an opponent last season; banned Pittsburgh's James Harrison for one game after a series of flagrant hits that culminated in a collision with Cleveland quarterback Colt McCoy's helmet; and has ramped up the amount of fines for what the league terms "egregious hits."
NFL spokesman Greg Aiello said before handing out any penalties, Goodell will review the information with his staff and consult with others, including the union and player leaders.
The players' union has not seen a full report of the investigation, so it can't be certain if Goodell will levy punishment under the on-field discipline or the personal conduct policy. There's a major distinction, because players can appeal on-field punishment to independent arbitrators Art Shell and Ted Cottrell. Appeals under the personal conduct policy are heard by Goodell and other league officials.
"The commissioner has broad authority to impose discipline for violation of league rules. We're not going to put it in a category right now," Aiello said.
The NFL hasn't cited specific players, but fines and suspensions are probable for those found to have participated in the bounty program.
"We take this issue seriously and we continue to look into it," union spokesman George Atallah said.
Goodell fined the New England Patriots $250,000 and their coach, Bill Belichick, $500,000 for the Spygate scandal in 2007, when the team was caught illegally videotaping the Jets' sideline. New England also was stripped of a first-round draft pick.
That violation pales in comparison to a bounty of up to $50,000 over the last three seasons that rewarded players for knocking targeted opponents out of games. The Saints can expect heavier sanctions than those given the Patriots, with suspensions likely for Loomis and Payton and a seven-figure fine for the organization.
"I don't think there can be a limited focus — if the league only is looking to penalize players and coaches," said George Martin, executive director of NFL Alumni and a former player, adding: "It is kind of shocking it still goes on in this time and age.
"The organization has to take responsibility for it because it took place under their jurisdiction," he said. "The league needs to do whatever it takes in the way of discipline to make sure this is stemmed."
John Lynch, an outstanding safety for 16 seasons, once was fined $75,000 for a hit on Indianapolis tight end Dallas Clark. Lynch was one of the hardest and surest tacklers in the NFL. He is just as sure that Goodell will hand out hefty punishments.
"I would expect this to be pretty severe and harsh because of the direction the commissioner has taken in making player safety if not his top initiative, then one of them," Lynch said. "If this is true, as blatant as this is, and to have a coach out there saying, 'You knock this guy out of the game. Get him taken off on a cart. Here is the monetary reward,' you need a severe and harsh punishment."
That coach has been identified by the league as Williams, who could face a year's suspension and a six-figure fine. Maybe more.
The Rams would not say Tuesday what duties Williams currently is performing.
"Coach Williams has shown contrition for his actions and continues to co-operate with the NFL in this investigation," Rams GM Kevin Demoff told the St. Louis Post-Dispatch. "Out of respect for the NFL's ongoing process, we will refrain from commenting until the league has come to a final decision on all aspects of this matter."
Williams could turn to the NFL Coaches Association for help. Its executive director, David Cornwell, was concerned about individual coaches being singled out.
"As this matter unfolds," Cornwell said, "I will work with our executive committee to protect the interests of individual coaches without compromising the NFLCA's fundamental belief that fair play and sportsmanship begins with the men who teach the game."
AP Sports Writer Brett Martel in New Orleans contributed to this story.