The literal translation is more like "my umbrella doesn't exist." (So since my umbrella isn't a thing that exists, there's no question of whether or not I have it.)
I think "I don't have my umbrella" would be something along the lines of "şemsiyem bende değil" ("my umbrella is not with me"), but I'm hoping a better Turkish speaker than I am can confirm that.
I am a little confused, because the translation of "Benim anahtarim yok" to be "I do not have my key" was accepted. Therefore I wonder why this does not apply for umbrellas!
"Benim şemsiyem yoktu"... how translate this sentence?? For example when I lost my umbrella, can I use this sentence:"my umbrella doesn't exist"
Like, if you didn't have an umbrella yesterday? You'd say, "I did not have an umbrella." (You just change the "do" from present tense to past tense.)
(And thanks for asking the question, because I didn't know how to say this in Turkish! =) )