There was one of my subordinates who was in tears after I corrected her mistake.
Were you calm and constructive when you corrected her?
I was calm and I told her what she did wrong and why it was wrong.
It sounds like you handled it professionally. It's best to accept criticism at work without taking it so personally. Some people are easily upset and there's not that much you can do.
I'm the worst boss ever.
No you did what you are suppose to do. As a boss you need to make sure people are working and not making mistakes.