If I met an unfamiliar word in a sentence, so that I did not understand the meaning of the sentence, can I say "I was confused by using the unfamiliar word"?
The way it stands, the sentence sounds like you are using the unfamiliar word. If by "met" you mean that you read or heard a sentence that someone else created, then you would want to change your statement.
The simplest would be
I was confused by the unfamiliar word
... along with the context of what you're talking about, that's perfectly fine and clear. It would also be important for you to have already said which word was unfamiliar; if you haven't, then the definite article "the" wouldn't be a good choice. You could also say
I was confused by your using the unfamiliar word
... but that's a little more complicated than it has to be. You could simply say
I was confused when you used the unfamiliar word.
In all these cases, if it's not important to say which word is unfamiliar, and the point is just that an unfamiliar word was present, you could use "an unfamiliar word."