If you're actually interested in the topic, here's an absolutely fantastic blog post on the subject:
http://blog.statuspage.io/why-public-apologies-suck
Some important bits:
>4 PARTS OF A BAD APOLOGY
- Justifying the offending actions or words.
- Blaming the victim.
- Making excuses.
- Minimizing the consequences.
>8 PARTS OF AN EFFECTIVE APOLOGY
- You actually have to use the words I’m sorry.
- Acknowledge that you messed up. (As in, “I take full responsibility for my words.”)
- Tell the person how you’ll fix the situation.
- Describe what happened, but without foisting the blame off on someone else.
- Promise to behave better next time.
- Make sure the person knows you know exactly how you hurt or inconvenienced them.
- Much like the first rule, it’s important to use some version of the phrase “I was wrong.”
- Ask for forgiveness.