I occasionally get search engine hits for some variant of "sad classical music", so I figure I could at least provide those searchers with a service. Earlier today I listened to a CD I recently purchased, a collection of works by Japanese composer Humiwo Hayasaka (on the Naxos label, in their "Japanese Classics" series).
The first work on this release is Hayasaka's Piano Concerto, which was composed in 1948. It consists of just two movements, a Lento and a Rondo. While the Rondo is fairly light-hearted, the Lento, which at more than twenty-two minutes is more than twice as long as the Rondo, is to my ears a terribly sad bit of music. According to the liner notes, the Lento is a "requiem for Hayasaka's brother and an elegy for the victims of World War II". It certainly feels like both of those things; the term I'd use to describe this movement is a "lament without words".
Anyway, there's some sad classical music for you.
(Excellent recording, by the way.)