Well before I had my first accident, I had learned here that for most of us, it's not a question of "if" but a question of "when". So far I have had no witnesses and only two outside of my home (not counting minor spillage or squish) .
I consider it a victory and not a cause for shame that you were able to rid yourself of your panties. Been there, done that. Consider what your options were -- where were you going to rinse them out -- in the toilet of a public restroom? In their sink? Yuck. Neither is a good option. People wrap up soiled diapers and toss them. This is the same thing.
Don't feel defeated if you can possibly manage it. We're all here for you. As a friend of mine said when I told him about
an accident I had, consider it a little dirt on a classic American muscle car.