Apologizing is admitting your mistake and showing your feeling towards the person.

It all depends on how you feel about the incident? Are you really sorry about what you did or happened? Or are you feeling sorry about how the person felt and is reacting towards the incident? Either way, an apology is a waste of words when you don't know what actually you are saying sorry for.

Now when you realized the what you are apologizing for let the person know about how you feel. And be done with it.

But never overthink such matter, Remember sometimes just a sincere apology can fix big issues before they get bigger.

regard
@inuke