Usage patterns
悔いが残るto be left with a lingering regret
He was left with regret, feeling he could have tried harder.
悔いのない〈事〉(a life, choice, etc.) without regrets
I want to live a life without regrets.
悔いを抱くto harbor a feeling of regret
She harbors regret over the choice she made when she was young.
〈事〉に悔いを感じるto feel regret about something
I still feel regret about that decision.