BBC Radio 4's flagship Today programme breached the broadcasting code when it aired the word "retard", watchdog Ofcom has ruled.
Crime writer Lynda La Plante made the remark after she was asked to discuss her induction into the Forensic Science Society.
Prime Suspect's creator said that she wanting to deny "a headline that apparently I call people at the BBC 'retards'."
The presenter Sarah Montague thought that La Plante, also responsible for crime drama The Commander, and Trial And Retribution, wanted to deny her use of the word.
But the author went on to say: "You do not send a script, full script, anywhere, you learn how to do a treatment, because you don't know if there's a retard at the end of that envelope reading it'. Suddenly I've called everybody at the BBC a 'retard'."
The BBC said that the presenter naturally assumed that La Plante was denying using an offensive term when she raised the question of the reported quote.
It added that when it became apparent that the clarification was "considerably less significant", the interviewer swiftly changed the subject, saying "moving on from that use of language".
The BBC apologised for any offence caused and acknowledged that ideally, La Plante would have been explicitly challenged on her use of the word during the live interview.
Ofcom acknowledged that there was an implicit criticism of La Plante's use of the word when the presenter abruptly changed the subject.
But it said that it would have been better if the presenter had addressed the issue with a more explicit statement and apologised to listeners for any offence caus
The media regulator said the incident breached rule 2.3 of the broadcasting code, on ensuring "that material which may cause offence is justified by the context".