Luis Suarez was "an accident waiting to happen" and the "time had come" for him to leave Liverpool this summer, according to Richard Scudamore.
Barclays Premier League boss Scudamore admitted he was not sorry to see Suarez join Barcelona, praising shrewd business from Liverpool in offloading the controversial Uruguay striker.
Catalan giants Barcelona prised Suarez away from Liverpool in a £75million transfer.
The 27-year-old was hit with a four-month ban from all football-related activity after biting Italy defender Giorgio Chiellini at the World Cup in Brazil.
Chief executive Scudamore conceded the Premier League will be a calmer place this season without Suarez, whose latest ban is his third for biting.
"I think probably the time had come," said Scudamore.
"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'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."
Suarez has appealed against his four-month FIFA ban to the Court of Arbitration for Sport, and will learn the outcome on Thursday.
The 78-cap striker was banned for 10 games for biting Chelsea's Branislav Ivanovic in 2013 and sidelined for seven matches for doing the same to PSV Eindhoven's Otman Bakkal in Ajax action in 2010.
Scudamore said the Premier League does not need "every world mega star" to continue to flourish.
Former Ajax striker Suarez netted 31 league goals last term, his departure leaving a chasm for Reds manager Brendan Rogers to fill, but Scudamore rejected suggestions the Premier League cannot retain its top talents.
"We lost David Beckham as well, remember, we do often lose one or two," said Scudamore, talking at the Premier League season launch.
Former Liverpool midfielder Dietmar Hamann echoed Scudamore's opinion that the club will be better off in the long term without Luis Suarez.
Hamann, speaking at a McDonald's and Football Association Community Football Day, told Press Association Sport: "I think Liverpool have bought well.
"I have always been very critical of Suarez's antics.
"In footballing terms, he is a big loss, but somebody else will score the goals and I think, long-term, they will be better off without him than with him.
"I'd rather have the six or seven players they have now than Suarez, because at the end of the day, if you want to win things, you need people you can trust, and he can't be trusted.
"If he does something stupid again, he could be out for years, or for good.
"Yes, he has been great, there is no doubt about it. But what could have been if he had not missed all the games he did when he was here? Maybe the team would have been in the Champions League a while ago.
"All he has to show from his time at Liverpool is a League Cup winner's medal (from 2011/12). He is not leaving a team that was ruling the Premier League or Europe during that the last few years.
"He is a player who scored goals, but at the end of the day they only got into the Champions League with him last season."
:: Dietmar Hamann joined kids at Burnage Metro FC in Manchester to celebrate the work of FA Charter Standard clubs at a McDonald's and FA Community Football Day. For more info visit www.McDonalds.co.uk/betterplay