Cleese added: "The audiences in Asia are not going for the subtle British humour or the class jokes."
Cleese believes the Daniel Craig Bond films are too full of action sequences.
Gadgets have also begun to disappear from the latest films.
The franchise took a darker turn in 2006 when Craig made his debut in Casino Royale. The character of Q was ditched altogether, and the closest Bond came to cracking a joke was when he greeted a barman's "shaken or stirred" query by snapping: "Do I look like I give a damn?"
Casino Royale's director, Martin Campbell, said at the time that he had tried to film "more realistic" action scenes, adding: "We kept away from gadgets. We couldn't suddenly have John Cleese storming in with a rocket car."
Cleese's brief run as Q followed Llewelyn's 36 years in the role, during which he supplied Sean Connery's Bond and his successors with ingenious spy gadgets.
After a hiatus, Q reappeared in the 2012 film Skyfall, played by Ben Whishaw. This time, the humour did not revolve around Bond fooling about with the gadgets, but centred on the fact that Q looked barely old enough to be out of short trousers.
Sir Roger Moore has described Craig as the finest actor to play Bond, but acknowledged that the films are far more action based than in his day.
He said of Craig in Casino Royale: "My God, he did more action in the first half - in the first second - of the film than I did in all the Bonds put together. He's brilliant." Of his own films, including The Spy Who Loved Me and The Man With The Golden Gun, he said: "I always felt you should let the audience share the joke."
Roger Moore in an early Bond film.
Cleese's comments shine a light on the importance of the Asian market to Hollywood film studios.
This year's Edge of Tomorrow, the £100 million Tom Cruise science-fiction blockbuster, performed poorly in the US but topped the box office in Indonesia, Taiwan and South Korea.
Casino Royale was the first Bond film to be shown in China, with Craig flying in to attend the premiere in Beijing.