The thing with "untranslatable" words is that their perfectly translatable, but the connotations surrounding them are completely different. What untranslatable then means in this context is that the listener of the translated version will /not/ understand the same meaning as someone listening to the non-translated version.
For instance, while the literal translation of shouganai is "it can't be helped," I'll translate it as "shit happens" in one situation, or "that's bureaucracy for you" (among other things) in another, depending on context. There simply isn't a reliable equivalent.
Also, imagine a scene (one that occurs every day at the end of my restaurant shift) where everyone is saying "otsukare" to each other. How should I translate that? Should I just have people yelling "TIRED" to the room? I'd have translated the word 'correctly' but not actually reflected the general feeling of "wow, we did it bro. Good job"
I'm currently learning Japanese. As I've learned these 'untranslatable words' of course I learned them through dictionaries and English explanations. As I saw them used and used them myself, though, they came to mean something different. I had to develop a new concept to compile them to, as it were. Now I find them difficult to translate back to English, and instead they have become new words in my vocabulary. It's why pigeon languages happen. (you should see the English spoken in the English-speaking office I worked at. It's stolen many Japanese words)