Suarez 'an accident waiting to happen': Premier League chief
Uruguayan striker Luis Suarez scored 31 goals for Liverpool last season, including a hat-trick against Cardiff City on March 22, 2014 - by Adrian Dennis
The Uruguay striker left Anfield for Camp Nou in a £75 million ($127 million, 95 million euro) after he was banned for four months from all football after biting Italy defender Giorgio Chiellini at the World Cup in Brazil.
Scudamore said the Premier League would be more peaceful without Suarez, whose ban was his third for biting.
"I think probably the time had come," said Scudamore talking at the launch of the Premier League season, which starts on Saturday.
"He's a great player and I'm not taking anything away from his talents: he was voted by both his own players and the media last year the player of the year and deservedly so.
"He's great to have but an accident waiting to happen, and if you spend your time trying to promote what's good about the Premier League, you're always waiting for the next thing to come along.
"And this one in the summer, although it was with Uruguay, although it didn't directly involve the Premier League, clearly it reflected on Liverpool as one of our great clubs and it reflected on us," he added.
"He's done his time here, but I can't say I'm sorry to see him go.
"I think it was good business on a number of levels from Liverpool to move Suarez on," said Scudamore.
Suarez has appealed against his FIFA ban to the Swiss-based Court of Arbitration for Sport and will learn their decision on Thursday.
The striker was banned for 10 games for biting Chelsea's Branislav Ivanovic in 2013 and sidelined for seven matches for biting PSV Eindhoven's Otman Bakkal in Ajax action in 2010.