You are human and you'll eventually slip up. You'll make mistakes that harm, hurt or just annoy your co-humans.
You'll need to apologize. You'll have to really apologize. Make it worthwhile! Be sure that your apology isn't actually adding insult to injury. Point out where you were wrong. Prove that you understand how the other person was hurt.
Let's eradicate the bad habit of "nopologies". Let's make it sincere.