Okay, so the automated house isn't exactly a character—but it's still pretty awesome. Think about how much having one of these babies would improve your life (or at least increase your intake of cigars…).
The house is really the only "character" in this story. We sympathize with the house just like we would with a human (or Martian) character, because Bradbury describes it like one: it has a skeleton, skin, and nerves (64). It even has a personality: it does things "carefully" and has "an old-maidenly preoccupation with self-protection" (14).
So we relate to the house as if it were a person, but do we like it? Would we want to spend time there? We kind of think no. The house may have a personality, but it's not a very nice one. It has an almost "mechanical paranoia," and it continues on "senselessly, uselessly" with its tasks. When a dying dog comes in, the house doesn't think "oh no, we have to help the dog"—it's just "angry at having to pick up mud, angry at inconvenience" (14, 16, 19).
You know what? This house is starting to sound a lot like some of the more unpleasant antagonists from the other stories. And so the real tragedy of this story isn't the end, when the house falls apart. By making us sympathize with but not love this house, Bradbury directs us to the real tragedy, which is that all the humans are dead, and that all of our wonderful technology couldn't save us.