Loomis and Payton, in their first statement since a National Football League (NFL) investigation unveiled the scandal last Friday, both confessed to having knowledge of the bounties and doing nothing to stop the program.
"We acknowledge that the violations disclosed by the NFL during their investigation of our club happened under our watch. We take full responsibility," the two said in a statement released by the Saints on Tuesday.
"These are serious violations and we understand the negative impact it has had on our game.
"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 were both named in the NFL's report, which said neither did anything to stop a bounty program that rewarded players with payments of thousands of dollars for hard hits that knocked opponents out of games.
NFL commissioner Roger Goodell, already trying to improve the league's image in the face of lawsuits by former players over concussion injuries, could hand down stiff fines, bans and forfeiture of draft picks.
Payton was named the NFL's coach of the year in his first season by turning a 3-13 Saints squad into a 10-6 team in 2006 that made the playoffs for the first time in six year. He went on to win a Super Bowl with the team in 2010.
Loomis was named general manager of the Saints in 2002 and was named the NFL executive of the year for 2006.
The report said former Saints defensive coordinator Gregg Williams administered the program, which violates long-standing NFL rules and is inconsistent with the collective agreement.
Williams, who became the defensive coordinator of the St. Louis Rams earlier this year, issued his own statement shortly after the NFL's report on Friday acknowledging his involvement.
"It was a terrible mistake, and we knew it was wrong while we were doing it. Instead of getting caught up in it, I should have stopped it," said Williams.
"I take full responsibility for my role. I am truly sorry. I have learned a hard lesson and I guarantee that I will never participate in or allow this kind of activity to happen again."
(Reporting by Frank Pingue in Toronto; Editing by Julian Linden)
