In his first public comment since he was suspended by the NFL for the 2012 season, Payton also vowed that there would no repeat of the practice where players were financially rewarded for injuring their opponents.
"Our organization will implement all necessary protections and protocols, and I will be more vigilant going forward," Payton said in a statement issued by the team on Friday.
"I am sorry for what has happened and as head coach take full responsibility."
Payton's apology came two days after the NFL handed down a series of punishments to Saints staff for their involvement in the brutal scheme.
Payton, the Super Bowl winning coach in 2010, was suspended without pay while the team's former defensive coordinator, Gregg Williams, was banned indefinitely.
General manager Mickey Loomis was suspended without pay for the first eight games of the upcoming regular season while assistant head coach Joe Vitt was suspended for six games.
The team was also fined $500,000 and will forfeit their selections in the second round of the 2012 and 2013 NFL drafts.
"I share and fully support the league's concerns and goals on player safety," Payton said. "It is, and should be paramount.
Respecting our great game and the NFL shield is extremely important to me."