Man is, at least from the physical perspective, merely a highly evolved animal. The ability to concentrate on a certain point on a wall for many hours at a time is in itself, while not apparently practical, a far more advanced use of concentration and attention than can be seen manifested by another animal.
The word "animal" can be used in the sense of a metaphor:
More "animalistic parts of the soul," for example, is synonymous with the literal "vulgar parts of the soul." The soul is not an animal nor is any part of it an animal, but the term "animalistic" is suitable to term vulgar areas in contrast with those erudite as vulgarity, being lower than piousness, can be paralleled with an animal and man.
It may also be used as a literal word. An animal is physically, and from what is observed, mentally lower than a human being. Therefore, "animals, not gods" can be used to compare animals literally with humans as gods or metaphorically to show the animalistic areas of the soul and the more "pure" ones.
Either interpretation suffices.