If someone asked me if I regretted something, how can I express if even his/her assumption that I regretted something surprises me? In my mother tongue I would answer with a question like "why would I have regretted it?", but in English it seems unnatural to me. What do you think?
It doesn't sound unnatural to me at all, although the simple present tense might be more appropriate than the present perfect if the question was posed in the present tense (which suggests that you might still be feeling regret up to the present moment):
Q. Do you regret doing it? (or Do you regret having done it?)
A. Why would I regret it?
The present perfect is better if the question was posed in the past tense:
Q. Did you regret doing it? (or Did you regret having done it?)
A. Why would I have regretted it?