We have two more simple vowels in Korean that don't have "y-versions."
sounds like the u in put and is Romanized as eu. In words of foreign origin, it is used to "fill in" a syllable and is barely pronounced; hence "Smith" would become "Seu-mi-seu"
sounds like the ee in meet and is Romanized as i. This is because the letter i sounds like ee in most European languages.
These don't have y-counterparts because the Korean language doesn't have any words that use those sounds.