The parts of an apology, in requisite order, are as follows:
1. I’m sorry.*
2. I feel [emotion word].
3. It sounds like you feel [emotion word] because you thought I said/did [restate what you heard].
4. (if applicable) That is not what I intended. I don’t think I communicated clearly. Are you willing to let me try again?
Failure to follow these steps may result in other people thinking you’re not actually apologizing.
* Mandatory field. No qualifiers allowed.