Steinbeck is sympathetic toward his characters, but he's not going to invent a happy ending for them. Instead, he contrasts the real world of poverty, limited resources, limiting social roles, human intolerance, and violence with the dream world of freedom, autonomy, wealth, friendship, and loyalty. This stark juxtaposition seems an honest attempt to reveal that for some, the American Dream was simply that—a hopeless dream.
Of Mice and Men is written in a naturalist style (See "Genre" for more about that). Since naturalism is about the most depressing literary style ever invented, we understand why the tone is dismal. For naturalist writers, characters are essentially "human beasts," victims of their surroundings. Think about how often Steinbeck refers to Lennie as an animal, comparing him to a "bear" dragging his "paws" (1.4) or "snorting into the water like a horse" (1.5). There's no moralizing about "good" or "evil": the naturalist writers sees his characters as controlled by environment, heredity, instinct, or chance.
Take Lennie: Lennie has some kind of mental disability, which (obviously) influences his actions. Though Lennie inarguably commits a terrible crime, the way Steinbeck portrays him makes us hesitant to pass judgment. Steinbeck presents the characters to us just as they are, never insisting that we think this or that about them. Instead, his approach makes us feel for them as fellow human beasts, caught in the inevitable suffering of existence.