grammar - Understanding why に particle means "because" in this sentence

I am struggling to understand the syntax of this sentence that I found in a grammar book.

あまりの言葉にあきれてものが言えませんでした。

I could not say anything because of the outrageously unkind words.

I read it as "not many words に outrageous thing が was unable to speak."
In other words, the pattern used to say "because of B I was C(action) A" would be "AにBがC(action)." Is this the correct understanding of this grammar?