I read this story when I was 10 or 11 and found it very moving.
An alien from a very advanced species crashes on Earth. He is trying to communicate with humans to get help. He looks like a very cute furry animal, and no-one will pay him attention except to put him into some sort of travelling carnival sideshow, from which he escapes. The end is tragic...he goes to live with rabbits in a field.
The story might have been called something like 'The Star Creature'.