The most common and most likely answer to this crossword clue is the 5 letter word ALACK
I've seen this crossword clue in Independent
A
L
A
C
K
More clues leading to the result ALACK
- A thing I don’t have, I regret to say!
- Vitamin deficiency generates expression of regret
- Need to pursue a cry of woe
- A jet won’t start, I’m sad to say
- A shortfall, I’m afraid
- Unfortunately need to support Austria
- Eating bit of chicken a la king? Oh dear!
- A need for old-fashioned expression of regret
- A need to give an old-fashioned expression of regret
- A shortage of woe!
Buddy explains!

The straight part
We know that "expression of regret" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case expression of regret = alack.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 ALACK mean?
ALACK interjection- An expression of sorrow or mourning.