In modern English, 'repent'/'repentance' is almost always used in a religious context, as christian bible-pounding preachers have been screaming for centuries, "Sinners repent!!!!!" However, if you look up the definition, you probably won't see any reference to this fact. 'Remorse' is a good synonym for the noun 'repentance', but doesn't have a verb form. For the verb 'repent' you can certainly use 'regret' and you won't sound ridiculously righteous.

Repentance is a noun meaning "remorse for your past conduct" while Regret if used as a noun means "sadness associated with some wrong done or some disappointment" however it can also be used as verb and it will interpret the same meaning like that of repentance...."feel remorse for; feel sorry for; be contrite about" i hope this will help...this I learned from Advanced English dictionary.