The most common and most likely answer to this crossword clue is the 15 letter word DISSATISFACTION
I've seen this crossword clue in The Daily Telegraph
D
I
S
S
A
T
I
S
F
A
C
T
I
O
N
More clues leading to the result DISSATISFACTION
Buddy explains!

The straight part
We know that "Regret" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case regret = dissatisfaction.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 DISSATISFACTION mean?
DISSATISFACTION noun- Unhappiness or discontent
- The cause of such feelings