The most common and most likely answer to this crossword clue is the 3 letter word SOZ
I've seen this crossword clue in The Times
S
O
Z
Buddy explains!
The straight part
We know that "I regret to say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case i regret to say = soz.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SOZ mean?
SOZ interjection- Shortened form of sorry.