I know you're Japanese, but I think you (and many Japanese) misunderstand the definition of "setsunai." Setsunai (切ない) means "圧迫されて苦しい。胸がしめつけられる思いでつらい。" Thus, setsunai has nothing to do with "sentimental" and would be best translated into English as "cruel" like Nyl said. Painful, bitter, and heart aches are good translations too, but in my opinion, "cruel" is the best.
There are some Japanese words that the Japanese themselves misunderstand the meaning of the words. For example, the majority of Japanese believe that "kosoku (姑息)" means "hikyona (卑怯な)" and is translated into English as contemptible, nasty, or mean. However, its correct meaning is "ichijishinogi (一時しのぎ)" and the equivalent word in English would be "makeshift."
Another example is "buzen (憮然)." Most Japanese think it means "harawo tateteiruyousu (腹を立てている様子)." To get angry with somebody or something. Its real meaning, however, is "shitsuboushite bonyarishiteiruyousu (失望してぼんやりしている様子)." Being in despair and at a loss.
Anyway, please look up the word "setsunai" in your Japanese-Japanese dictionary. It says setusnai means cruel, and Nyl's answer is the best!