Regretted, say, being offensive (4)
I believe the answer is:
rude
'offensive' is the definition.
(thesaurus)
'regretted say' is the wordplay.
'regretted' becomes 'rued' ('rue' can be a synonym of 'regret').
'say' shows a homophone (sound like).
'rued' sounds like 'RUDE'.
'being' acts as a link.
(Other definitions for rude that I've seen before include "Impolite - simple" , "Impertinent" , "Blue" , "lacking refinement" , "likely to offend" .)