The theatre impresario, 74, did not attend the closing show at the Gillian Lynne Theatre in London’s West End on Sunday.
Instead, director Laurence Connor appeared on stage alongside the cast to deliver a message from the composer about the production’s premature end.
After a backlash at the content of the letter, specifically where he made reference to a “costly mistake”, Lloyd Webber issued a statement saying: “I am devastated to have been reported to have said that my beloved production of Cinderella was a ‘costly mistake’.
“Nothing could be further from the truth, and I am very sorry if my words have been misunderstood.
“I adore this production and I am incredibly, incredibly proud of Cinderella and everyone who has been involved in our show.
“We were desperate to support the West End after 2 years of a devastating pandemic and the mistake we made was trying to open too early, meaning we had to postpone twice.
“Everything we did was to try and support the West End and get everyone back to work after the worst period in our history.
“For now, I want to say thank you to everyone involved in Cinderella for all you have done.
“With love today and always, Andrew Lloyd Webber.”
The statement followed a comment from a spokeswoman for his company The Really Useful Group, who also said the reference did not refer to the production itself.
She said: “The reference to a ‘costly mistake’ was never, and would never be, about the production.
“It related to the early opening of the show and the myriad challenges faced because of the Covid-19 pandemic, which the full text makes clear.
“As Andrew said in the letter, he is immensely proud of the show and that is hugely due to everyone involved.”
Last month Lloyd Webber announced Cinderella, which starred Carrie Hope Fletcher in the lead role, would be closing, less than a year after it premiered.
In the letter, read out to the audience at the Gillian Lynne Theatre, he said: “I am hugely sorry not to be able to be with you today.
“But I want to thank everyone, our fabulous cast, crew and musicians, the superb creative team, Laurence, JoAnn, Emerald, David and Bruno to mention just a few, and everyone who works in Really Useful and the Gillie for bringing Belleville brilliantly to life.
“I once wrote a song with the late great Jim Steinman called If Only.
“I keep thinking, if only we had opened three months later we wouldn’t have had to postpone our opening twice because of Covid. If only we hadn’t had to close for a month over Christmas and New Year, once again thanks to Covid.
“And if only we had had a crumb of help from the Recovery Fund, I promise you we would have been here for a very long while to come.
“Anyway, my huge thanks to everyone. We kept the government’s feet to the flame and lead the charge to get the West End open again.
“It might have been a costly mistake, but I am proud that we did and proud of everyone who supported me. Cinderella got some of the best reviews of my career.
“I am immensely proud of it and it’s hugely due to you.
“All my love, Andrew.”
The show’s premiere took place in August last year, having been scheduled for the previous month but delayed due to Covid isolation protocols.