I think you might be having the wrong takeaway, or at least an unhelpful one.

The emotions you felt were normal to feel. And I totally understand not wanting to feel that way. But the path forward is learning how to process your emotions in a healthy way (note: this does not mean the same thing as "learn to stuff away your emotions").

Anger is often a reaction to feeling wronged or misunderstood, it can be helpful once you have calmed down from the initial spurt of anger, to sit with it and try to think about what exactly the reason is you are angry. If this situation had happened to me, my anger would probably have been rooted in feeling rejected/abandoned (this is something I have a particular issue with, so that makes sense). For you, it might be the same, or something entirely different. Figuring out why you felt angry is the first step to being able to process what you're feeling. You can then try to turn whatever your findings are into a plan for the future, should a similar situation happen again, or if applicable, prevent/reduce the likelihood of it happening again.

In a way, making this exact post you've made is actually you trying to take measures to prevent yourself feeling this way in the future. It's kind of meta, but helpful.

Others have mentioned that you might broach this topic with your therapist, and I agree. Keep it to how it made you feel, don't say anything about your therapist. "I felt let down when you missed our appointment. I felt ever more helpless because I had no notice. Do you think it would be possible to have some notice in the future, if you must miss or reschedule a session?" that kind of thing. Others also touched on what to do if this is a routine thing for the therapist, and I'll leave that to them.

I read most of the other comments and I didn't see this sentiment but: genuinely, give yourself props for noticing an issue, and seeking a way to fix it. And, give yourself props for seeking therapy. You are doing the right thing. Today wasn't your fault and you haven't "failed" at the first step. You deserve to feel proud of yourself. Keep going.