Failing at negotiation (how to learn from it?)

Hi Brooke,
first – thank you so much for the answer to my last question. It was extremely helpful! So here’s my next question: How do I become a better negotiator? Or: How do I have my own back? I really could need some of your wisdom here.
Let me explain: Last week I sold part of my business (= step one to move forwward). All was good. But then, at the end phase of the negotiation the “buyer” said: “Just one little thing. The price is too high. By chance, I know how much other people payed in similar situations, and it was x” (ca. 10% less of what I wanted to have). I said something like “let’s meet in the middle” without even defending my original price. So we met in the middle and I still am angry with myself. Why did I do that? Why didn’t I stand for myself? Not even trying to? But then, I don’t want to be mad about myself, but learn – I really think, understanding this situation will help me with the next steps to go for my impossible goal. But I will need to get it… so here’s my understanding so far:
C: y says: I only want to pay x
T: maybe she’s right and my price really is too high?
F: fear (she might leave the table)
A: saying “let’s meet in the middle”
R: paying for less than I wanted

Intentional model:
C – same
T – that’s the price I want. Too bad, if she doesn’t want to pay it. I’ll find another solution (fact is, I couldn’t have found anouther buyer, due to a complicated legal situation)
F: confident
a: Stick with my plan. be as convincing as I can be – and probably I would have gotten “my” price

I see, that this is possible. But how do I get myself into that place of confidence, when the circumstance is not in my hands? Like, if she had gone out of negotiations, it would have been hard to continue with my crazy goal (of course not impossible, but much harder than losing those 5% of money). Would love to hear your thoughts on this.
Thanks so much!