"Even though I knew it couldn't go anywhere [because] these things never happened, there is always the fear and the embarrassment of being talked about in those terms.
"I'm moving on with my life."
The singer was the subject of a long-running investigation by South Yorkshire police, which centred on accusations made by four men.
He was never arrested or charged, and always maintained his innocence.
The claims against the singer were dropped on 16 June on the grounds of insufficient evidence. The CPS reviewed the case following an application by one of his accusers but concluded this week that their decision has been correct.
Sir Cliff was speaking to BBC Radio 2 after announcing the release of a new album, Just... Fabulous Rock 'n' Roll which will feature a duet with Elvis Presley.
Recorded in Nashville, it is Sir Cliff's 45th studio album, and his 101st overall, and comprises new versions of classic rock tracks like Wake Up Little Susie, Rave On and his own debut single, Move It.
He said it was time to return to "the thing I love best" on the record, which celebrates "a more innocent time".
"There is an audience out there of a certain age group, and they're not going to stop loving the music they liked when they were 14," he told Radio 2. "And I'm one of those people."
"Yes, every now and then I hear something that I like from today but, for me, it never really stands up to the music of the Everly Brothers and Elvis and Jerry Lee Lewis."
Elvis appears on a new version of Blue Suede Shoes, with Sir Cliff's voice mixed with archival recordings of "The King". The track was made with the approval of Presley's estate.