Manchester United, Liverpool, Arsenal, Chelsea, Manchester City and Tottenham all signed up to the controversial tournament on Sunday before withdrawing 48 hours later.
Uefa president Aleksander Ceferin vowed to “rebuild the unity” of European football after the six Premier League sides stepped away from the plans on Tuesday evening, and the clubs are not expected to be hit by either financial penalties or competitive sanctions.
Ceferin had taken a strong stance against the Super League following the public announcement of the proposed breakaway, and called accused Manchester United executive Ed Woodward of being a “snake” for his role.
Sutton has urged Ceferin to back up his words with strong actions, however, and believes the Super League will come around again unless the clubs involved are punished.
“I’d give them a 12-point deduction immediately and I’d give them a European ban for a couple of years,” Sutton said on BT Sport.
“Aleksander Ceferin called them snakes, well take the venom out of the snakes. Give them a European ban, let other teams come up and compete. Otherwise what is the deterrent?”
Sutton said it is important for the English clubs to remain in the Premier League but with reduced powers, and has called on the owners of those involved in the Super League plot to put money back into the game as a form of retribution.
“If you expel them from the Premier League they can go and set up their own other league,” he added.
“I think there are things which can be done. How do you punish a billionaire? I think we can fine the billionaires heavily and put the money into grass roots football, say £50million per club.
“What we have to do is take away the power from these billionaires. Don’t let them become anywhere near the decision making process. These six clubs didn’t think about the other clubs. Take the power away from them.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies