I think we do have animals that understand higher consciousness. Dogs!
Over time, domesticated wolves figured out that humans were more advanced because they consistently had access to food and shelter while wolves had to hunt for it. By adapting their own behavior to fit in with the superior species, we wound up with today's dogs who largely choose to be servile because it's advantageous to them. Isn't that an example of recognizing a higher species and submitting to it?
The "how they know, how we know" question is clear, too. Dogs knew we were smarter because of what we were able to accomplish and provide. If a "superior" alien race showed up and could do stuff we couldn't, we'd think they were smarter, too.
Language and adaptability play a big part, too. Cetacean language certainly helps them survive, and so does primate language. But human language went far beyond any other species and allowed man to cooperate and coordinate adaptations, like creating a building and heating it to survive the cold. Or inventing transportation to move to a more desirable living space. No other animals have pulled that off at that level.