The Rain Man actor stepped behind the camera for his directorial debut, which features Smith, Courtenay, Billy Connolly and Pauline Collins as retired opera stars.
Courtenay reveals the cast delivered a rendition of Verdi's Rigoletto for the film, but the footage ended up on the cutting-room floor as it wasn't their best work.
He tells Britain's Daily Mail, "Dustin did a great job on the movie, but sadly he had to cut out our singing performance.
"We tried singing during filming, but when it came to what the public sees, we thought it was the best solution not to hear our quartet. The fact is some of us were better than others."