A thing I don’t have, I regret to say! (5)
I believe the answer is:
alack
'i regret to say' is the definition.
(expression of pity similar to 'alas')
'a thing i don't have' is the wordplay.
'thing i don't have' becomes 'lack' (something lacking or missing).
'a'+'lack'='ALACK'
(Other definitions for alack that I've seen before include "Sadly" , "unfortunately" , "Alas (archaic)" , "I mourn" , "I'm sorry to say" .)