The point is not to ask for Mechila. The Lashon you’ll find in Shas and Halacha is to be Mefayes him. Piyus means to apologize and to make the person feel better by explaining that you truly regret what you’ve done and you will try to make up for it.
Also, Shaas Kaaso does not count and is actually a form of Onaa. Shaas Kaaso will have to be calculated in each case separately. If the pinch is still hurting do not ask for Mechila. What did you you do for that person that he owes you a Mechila Gemura Beleiv Shalem? Not only did you wrong him, now he owes you for it, too!?