Final Ivory Coast squad for World Cup
Kone, a regular over the last six years, midfielder Emerse Fae and defender Abdoulaye Meite were among the victims as Eriksson whittled his squad down from 30 to the required 23.
The squad sees the return of Sevilla midfielder Christian Koffi Ndri, better known as Romaric, who had been surprisingly left out of the squad that went to January's African Nations Cup in Angola.
"It's always sad when you have to tell seven players they have to go home. It's not the best part of a manager's job but it has to be done," Eriksson told reporters at the tiny Swiss village where the Elephants are training.
"It's difficult but at the end you have to make the decision," added the former England manager who looked glum, despite remaining his usual calm self.
"I talked to the seven players here in this room - not pleasant.
"From what I have seen of the players, they are all extremely well-educated, happy people and they took it as men with style. I thank them for what they have done for us and I wish them luck in the future."
Eriksson, appointed in March after Vahid Halilhodzic was sacked following a quarter-final exit at the Nations Cup, had only one full week with his squad before making the decision.
The Elephants were held to a 2-2 draw by Paraguay in a friendly on Sunday, his first match in charge.
The diminutive Kone has 44 caps and nine goals for Ivory Coast, played at the last World Cup and this season helped Olympique Marseille win French Ligue 1.
The omission of Meite, who plays at West Bromwich Albion, was also a surprise.
Eriksson included Seydou Doumbia who was topscorer in the Swiss Super League this season with 30 goals for Young Boys Berne but has only five caps and one goal for his country.
The only Ivorian-based player was goalkeeper Daniel Yeboah, who has not played for his country in the last seven years after being blamed for a loss to South Africa in 2003 that cost a place in the Nations Cup finals.
Ivory Coast face Brazil, Portugal and North Korea in arguably the World Cup's toughest group and Eriksson has inherited a squad which was reportedly suffering from internal rifts.
"If we don't have the right spirit, we don't need to go to the World Cup," said Eriksson.
"That's something we have to work on together with the players because the spirit is the most important thing.
"I don't like to talk myself but, if I'm good at anything, I usually create a good atmosphere.
"I do it by doing the right kind of work, talking the right way to them, by being myself.
"The most important word is respect. You have to respect each other, they have to respect the kit man, they have to respect the ladies cleaning the room... if you don't have respect something is wrong.
"It doesn't matter what your name is, or how much you earn or where you're playing football. All 23 are the same.