The NFL said it had informed the Saints the suspensions would remain in place. Payton will sit out the 2012 season and can return to the team April 16, 2013.
New Orleans General Managers Mickey Loomis was suspended for eight games and assistant coach Joe Vitt for six games in the 2012 season.
Each had appealed the original disciplinary action to Goodell last week.
An NFL investigation determined the Saints' defense under Williams operated a system in which players were given cash bounties for plays that injured or caused opposing team members to miss playing time. The period includes New Orleans' run to a win in Super Bowl XLIV.
In addition to the personnel suspensions, the Saints were fined $500,000 and second-round draft picks in 2012 and 2013.
Still to be determined are possible penalties for players found to have been involved. The NFL Players Association is conducting an investigation. The NFL has said as many as 27 players may have taken part in the bounty system.