Radical_Dreamer is correct: Making an apology is a genuine act of penitence. You're not supposed to get anything out of it other than a clearer conscience. If the offended party takes your show of contrition and rewards it with forgiveness, then it's a bonus.
Asking for forgiveness is the same as asking for a favor, except you're asking this favor of someone who you just wronged. Such requests, then, ought to be judicious.