The viewer from Finchley, north-west London, was one of three who complained. He described the joke as “at worst unequivocally racist” and a “horrible jibe”.
In response, the BBC’s complaints department wrote to him, referring to the issue of “bad language” rather than racism.
The letter said that “bad language” was sometimes used in programmes to reflect “plausibly the way people actually speak”.
It added: “It is inevitable that programmes which are acceptable to some will occasionally strike others as distasteful”.
The BBC “would never deliberately set out to cause offence”.
The viewer said he had called the BBC pointing out its failure to answer his accusation of racism, and was awaiting a further response.