Take a step back. Relax. Get a little distance. (I know it's hard).
bcr229 is absolutely on it.
You are handling it in such a mature fashion (owned it, apologized, new plan of action so it doesn't happen again), if you worked for me, I'd value that level of maturity a great deal.
Maybe bring in a token for the people who covered your shift, a coffee or donut holes...nothing big, just a token to show you appreciate them. (Do it even if they were less than gracious - you'll be pleasantly surprised!)
And go hug a reptile. 8^)