Manchester City chief executive Ferran Soriano says the club lost their values when signing up to play in the European Super League.
Fan backlash and threats from UEFA, FIFA and national governments but a stop to the breakaway league within days.
City were the first team to announce their withdrawal from the competition on Tuesday, before others followed suit.
"I am writing to you regarding the event of the past few days," Soriano said in a letter to City supporters.
"I am sorry it has taken a little time, but the circumstances have been somewhat exceptional and it was important to me to contact you directly.
"As you know, Manchester City has formally enacted the procedures to withdraw from the group developing plans for a European Super League.
"As always, when we make choices and decisions, we do so with the best interests of the club in mind and we believed that being part of such an initiative could give us a voice that might be imperative to our future ability to succeed and grow.
"However, in making that choice we failed to remind ourselves of the unbreakable link between the passion of our fans and the right to have the opportunity to earn success.
"It is a truth that is fundamental to the DNA of Manchester City, and the board deeply regrets taking a decision that lost sight of the historic values of the club. We made a mistake and we sincerely apologise to our fans for the disappointment, frustration and anguish caused by the last 72 hours.
"The owners, chairman, board and staff are completely committed to ensuring that the club continues to contribute meaningfully to the ongoing well-being of both the English and European football pyramids and their associated competitions.
"We will embrace the opportunity to earn back the full trust of our stakeholders and the football family in general."