I feel bad about what I said
Why do you feel bad about it?
I feel bad because I embarrassed myself.
The fact you recognized it is good. Since it's unlike you, most people will realize you probably spoke a little too freely and will forget about it by tomorrow.
I hope they do, but what if they don't forget about it?
Everyone forgets things eventually, even if it takes a little while. Try not to stress out about embarrassing yourself, it happens to everyone.