In January, the singer scrapped her dates 24 hours before opening night, telling fans the show was not ready.
Speaking to BBC Radio 4's Desert Island Discs, Adele said postponing her three-month residency left her "devastated", but said she stood by the decision.
On Friday, she told fans the shows would be rearranged "very, very soon".
Speaking to Desert Island Discs presenter Lauren Laverne, the 34-year-old said: "I definitely felt everyone's disappointment and I was devastated and I was frightened about letting them down.
"I thought I could pull it together and make it work and I couldn't, and I stand by that decision."
She continued: "I'm not going to just do a show because I have to or because people are going to be let down or because we're going to lose loads of money. I'm like, the show's not good enough."
The singer, who released her fourth album in November, was criticised online after breaking the news in a tearful last-minute Instagram video that the Caesar's Palace shows would not take place as planned.