followed with ‘I wasn’t aware is so important to you. I didn’t want to insult you and if you felt so, I apologize. The word fuck is one I use very often, but I’ll try to control myself around you’
Note I didn’t insult the coworker (no fuck you or fuck off), but simply said ‘fuck’ out loud due to a job error.
It’s pretty straightforward. If the apology is expressed around how the other person perceives things. It’s not a real apology.
I’m sorry you feel that way. I’m sorry you think that. I’m sorry you took that misunderstanding from me.
In fact, in these situations, it may be better not to apologize at all. I realize some of the language I use isn’t great, I’m working on it, please understand I’m not going to be perfect at it.