Uruguay's Luis Suarez, who was suspended from all football-related activity for four months after biting Italy defender Giorgio Chiellini during the World Cup, joined Barca in July for a fee put at 81 million euros ($108.35 million) by local media.
His move from Liverpool follows a season where he finished as Premier League top scorer with 31 goals and won the English PFA and Football Writers' player of the year awards.
But, having already served bans for two previous biting offences and another for racially abusing then-Manchester United defender Patrice Evra, Premier League chief executive Scudamore welcomed his exit from English soccer.
"I think probably the time had come," Scudamore said of the 27-year-old forward's move, speaking at the launch of the new Premier League season on Wednesday.
"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 taken his appeal against his latest ban to the Court of Arbitration for Sport, who will announce their decision on Thursday.
Scudamore, 54, has been in charge of the Premier League for 15 years and has overseen a huge increase in the value of its television rights at home and abroad.
That money has helped to make the English top flight the most lucrative league in the world but, along with Suarez's departure, England's domestic game has seen top talents like Cesc Fabregas and Cristiano Ronaldo switch to Spain.
He says losing some of the world's best players is an inevitability considering the financial might of Barcelona and Real Madrid but the Premier League can still prosper even without players of Suarez's ability.
"We lost David Beckham as well, remember. We do often lose one or two," said Scudamore.
"The truth of the matter is the Spanish system producing those two very wealthy clubs, because of the way they sell their individual television rights, have always had the economic power.
"It's not just the way they sell their TV rights, it's their political organisation and how they go about finding money they haven't got.
"We've not always had the absolute top name at any given time in world football, but we've got enough in the top 50 of the world's best players.
"And we've certainly got eight of the world's top 20 clubs, and that's the most important thing for me - we've got 20 competitive clubs.
"Economically we've got 20 of the world's top 50 clubs now... And that to me is more important in many ways, that the matches are competitive.
"We've got enough stars, and we don't need absolutely every world mega star name to make this a successful league."
The Premier League season starts with Louis van Gaal taking charge of his first competitive match as Manchester United manager against Swansea City at Old Trafford on Saturday.
($1 = 0.7476 Euros)