I don't understand. They have a stage and formal performances in Kindergarten? I don't recall my daughter or my granddaughter ever being asked to perform. They did do presentations for open house, grandparent's day that sort of thing and all of the kids did something, most of them as a group. Sure, once in awhile there would be a little ham who would act on their own but it just seemed to come naturally.
You say she cries when she's not asked. Does she cry at school or at home? IF she's crying only at home, I'd take that as a clue to reassure her it doesn't matter to you. It sounds like she's sorry she disappointed you. If she cries at school talk with the teacher about it.
You cannot make your daughter happy all of the time. Perhaps this is one of those situations in which she'll learn how to handle her disappointment.
I'm also wondering why it's important that she perform, why is she upset? There are other kids in her class who are shy. Do they cry? Are they upset?
I'm thinking I just don't understand the circumstances in which she cries. In my experience, teachers encourage the shy ones to participate. Again I don't understand where a stage comes in. As children get older they do have talent shows and plays but the kids build up to those gradually over the first few years. I just cannot think of a time that a kindergarten student would have frequent opportunities to perform on stage. The kindergartners at my granddaughter's school sing as a group when there is an assembly at which students perform.