The lengthy suspensions given to current Saints Jonathan Vilma and Will Smith, as well as ex-teammates Anthony Hargrove and Scott Fujita, were justified, the commissioner said in rejecting their appeals.
Vilma received the harshest penalty -- suspension without pay for the entire 2012 season.
"Throughout this entire process, including your appeals, and despite repeated invitations and encouragement to do so, none of you has offered any evidence that would warrant reconsideration of your suspensions," Goodell wrote in the decision.
Instead, he asserted, the four players "elected not to participate meaningfully in the appeal process" by refusing to make official statements or question their league accusers.
League sources have said investigators collected voluminous evidence that Saints players were awarded bounties for intentionally injuring key opponents.
The NFL Players Association said Tuesday Goodell's move demonstrated "a lack of fair due process, lack of integrity of the investigation and lack of the jurisdictional authority to impose discipline under the collective bargaining agreement."