Use the adjective sorrowful to describe a sad feeling, especially when it involves grief or loss. You feel sorrowful when you lose someone you love.
Sorrowful is a melancholy adjective: when your heart is broken, you are sorrowful, and when your beloved cat dies you're also sorrowful. There is a sense of permanent loss behind the word sorrowful. It comes from the sense of being "full of sorrow," and the ultimate root is the Old English word sorg, which means "grief, regret, trouble, or care."