I know that this depends on the workplace culture, but I've gone the other way on stuff like this because apologizing makes certain people smell vulnerability and never let it go.

I'm happy to explain what happened, and I'm happy to suggest improvements for avoiding a similar accident in the future. If you think I screwed up, chew my ass or write me up. Past that, it is what it is, and if you hold it over my head like a nagging parent, I'm going to use my outdoor voice.