I think it comes down to "failure" vs. "feedback." I don't look at a negative encounter as a failure. It's just feedback.

I ask myself, in a non-judging way, "what could I have done differently?" Sometimes the answer is "nothing" - you just caught someone on a bad day. But sometimes there are some things I can change about my behavior. If so, I try to incorporate that and go forward.

Whatever happened has already happened. You can't go back and change it, so there's no point in ruminating on it. But you can change how you behave in the future, and that's what a lesson is for.