Is the statement the smaller the animal the simpler the animal generally true?

This statement is not precisely true. For example shrews and mice are considerably smaller than humans and yet their organ systems are almost the same. Humans have the unique feature of a larger brain but mice have a more highly developed sense of smell and other adaptations. Different types of complexity that suit the environmental niche they fill. Comparisons between mammals show obvious similarities regardless of size.

Comparisons between various Phyla yield large simple animals and small complex ones.

The term "smaller" refers to threshold limits based on the number of cells the animal has and it's genetic complexity as opposed to physical size. Caveat: Some comparatively simple animals have many more chromosomes than much more complex animals so number of chromosomes is not a direct indication of complexity.

Single celled animals cannot compare in complexity to animals such a the rotifer which has a few hundred cells and can reproduce sexually or parthenogenically, has some discrete organ systems
and various methods of locomotion.