"If I wrote that song today, maybe I'd think twice about it.
"On the last tour, I wrote a new verse about censorship, but what's the point of that? So I've decided I'm not going to play it."
Costello is referencing a verse he rewrote for the song in 2013, in which he sang about being "cut down by the censors".
While it played uncensored on-air for decades, the word has been bleeped out in recent years, which Costello said "makes it worse".
"[It] is a mistake. They're making it worse by bleeping it for sure. Because they're highlighting it then. Just don't play the record," he added.
Costello's career has spanned more than five decades, in which he's won multiple awards including Grammy Awards in 1999 and 2020, and has twice been nominated for the Brit Award for Best British Male Artist.
He was inducted into the Rock and Roll Hall of Fame in 2003, and a year later was ranked at number 80 on Rolling Stone's list of the 100 Greatest Artists of All Time.