If I had (hadn’t) V3, SUBJECT would (wouldn’t) have V3.
I wish I had V3
I regret having V3 / not having V3 (to have V3 / not to have V3)
I regret that I V2
I should have V3
I ought to have V3
If only I had done my homework, my teacher would not have been angry.
I regret that I did not do my homework.
I am sorry I should have done my homework.
I am sorry I ought to have done my homework.
I wish …
I would (wouldn’t) have …
I regret being rude and underestimating you.
I wish I hadn’t made that mistake.
I am so regretful about it.