Sometimes a simple apology isn’t enough, let alone a simple “pardon me.” At those times you’ll need to talk the language of forgiveness. Fortunately for us, we’ve already done that. Remember بَخشیدَن (bakhshīdan)? Remember how بِبَخشید (bi-bakhshīd), its imperative form, can mean “pardon me”? Well, “pardon” being somewhat synonymous with “forgive,” بَخشیدَن also means “to forgive,” and that means that if you’re seeking forgiveness, بِبَخشید is the way to go. “Forgiveness” is بَخشِش (bakhshish), and one who is “forgiven” is بَخشیده (bakhshīdah, “to be forgiven” is بَخشیده شُدَن, bakhshīdah shudan). “I forgive you” would be شُما را می بَخشَم (shumā rā mī bakhsham).
I would be remiss if I didn’t mention that, yes, there is also a way to do this with a borrowed Arabic word, but it’s far less common. Remember the Arabic root عَفا (ʿafā), from which we get the Arabic for “pardon me” and “you’re welcome”? Well, عَفو کَردَن (ʿafū kardan) combines that root with, yes, کردن, to give us a verb that also means “to forgive.”