My dude, I'm no parent, but I am human. And as one human to another, you're allowed weakness and blow-ups and for stuff to irritate the holy living fuck out of you for no discernible reason.

The important thing is, you realized your mistake and you dealt with it like an adult. It's good to admit our mistakes, especially in front of others. You ultimately did the right thing. Remember the experience for the future, but go easy on yourself too. :)