Translation:I did not use an umbrella.
It is not a poor translation, especially when there isn't any context. It's not unbelievable that simply opening an umbrella may not entail putting it up, over one's head.
When it is raining, no, we would not likely say "put up" for a hand-held umbrella, at least, not in the U.S. Instances of such use can be found though.
Now, consider this sentence from Tatoeba:
Which is translated as :
"She put up an umbrella against a scorching sun."
Here, it makes perfect sense, being used as a shield more so than a shelter. I feel that "opened up an umbrella against" would sound more poetic, but not any more correct.
Now, suppose we are on a beach. What would you do with a beach umbrella? Surely, as it must be stuck into the sand it must be put up, in order for it to stand on its own. The same would be said when installing a patio umbrella. If it were already installed, then surely "open" would be more appropriate.
Remember, the English you know isn't the only English. If something sounds odd, perhaps you should look into it rather than just assume it is wrong because you've never come across it.
Edit: Wow I sure think those downvotes are unwarranted. I guess people don't like to feel wrong. Or educated. ¯_(ツ)_/¯
Are you trying to say that a beach umbrella would use a different word in Japanese, or that opening one would use a different word? Even if that were the case, it does not change the fact that "put up" is said in English to to refer to to the idea of opening an umbrella and positioning it above one's head; the latter part being somewhat important as one can open an umbrella without putting it up.
A beach umbrella was used simply for an additional example of a context that people might not even think of to illustrate that it is not bad English as people seem to think. Furthermore, I do not see why a beach umbrella would be omitted from Japanese lessons or why that is relevant when I was specifically giving examples of English usage of the translation in question. I am aware that 傘 is not ビーチ・パラソル and that the latter is not present in these lessons.
Forgive me if my assumption is incorrect, but English does not appear to be your native language. While I generally would not like to use that as an indicator of one's competence in a language, it is mine, and I quite know what I am talking about here; "put up" is perfectly valid. Some people seem to feel that that makes is seem like one is "putting it away", but at least where I come from, we just say "put away". Dialects.
This is the internet. Do I really need to waste my time citing references that can be found easily enough? Apparently this is common enough because there are a lot of queries for this exact issue to be seen with a simple search.
Dang yall are intense. Its ok if it's not directly translated! Theres a lot of things in japanese thats not directly translated. For example: おげんきですか？ directly means "are you healthy?" But we use it in the way of saying "how are you?". Or even こんにちは、literally means "this afternoon", but we translate it to good afternoon or hello. So its ok of the translation isn't exact, as long its the general meaning and we understand then it's ok!