Burton's adaptation of the Stephen Sondheim musical features Johnny Depp as Sweeney Todd, a barber bent on retribution over a lost love.
"It speaks well to Johnny's reputation that everyone went along with it," Burton said in an interview in Saturday's Los Angeles Daily News.
Burton said the movie's producer, Richard Zanuck, was hesitant about hearing Depp sing for the part, but Burton said Depp shined in the role.
"I didn't know what to expect. And when I finally heard him, I was amazed. It's a hard musical to do, and he just made it his own," he said.
The pair discussed the difficulties of filming to a prerecorded vocal track, noting that none of the scenes were lip-synched.
"The first thing you discover is that there is no such thing as lip-synching. You've got to belt it out to the music," Depp said in the interview.
The duo joked that Depp's vocal performance may launch a new Johnny Depp album, the newspaper said.
"He's got a big recording contract in Germany. He's going head to head with David Hasselhoff," Burton said.
2014: The Year in Music [PHOTOS]