I can understand and appreciate the embarrassment. But seriously, in situations likes this, just remind yourself, no one died. You're not a surgeon who lost a patient. I've seen some SERIOUS blunders with terrible financial ramifications but all these things at some point just become a story that's told with no person attached to it. But the most important thing for this to hold true, is to take responsibility....you'd be surprised how forgiving people are when you say I messed up, I'm sorry, how can I fix it. It's the ones who mess up and then create so much drama blaming others and deflecting that tank their reputations and are talked about for years.

I also use this 'tool' when trying to assess how much emotional energy/embarrassment/stress I should attribute to an incident. I ask myself will this matter in 10 mins, 10 hours, 10 days, 10 months, 10 years. That usually quickly puts things into perspective for me.

Sounds like it all worked out your way. Well done realizing your mistake and immediately escalating.