A proper apology

consists of conveying the 3 Rs:

regret (genuine empathy with the other)

responsibility (not blaming someone else)

and remedy (your willingness to fix it).

A good rule of thumb is to take the word that out of your apology. Instead of saying, “I’m sorry that…”, start by saying, “I’m sorry I…” This acknowledges upfront that you were the one responsible for the hurt and goes farther than “I’m sorry that you feel that way” ever will.