What is Regret ?
Regret is (noun) being sorry I have absolutely no regrets about what we did. She showed no regret for having made so much mess. much to someone’s regret making someone very sorry Much to my regret I will not be able to go to Chicago. Much to the children’s regret or much to the regret of the children, the ice cream van drove away. (verb) to be sorry that something has happened I regret to say that you were not successful. I regret the trouble this has caused you. We regret the delay in the arrival of our flight from Amsterdam. We regret to inform you that the tour has been cancelled. (NOTE: regretting regretted)
source: Easier English, Student Dictionary Upper Intermediate Level