Is there a specific term to refer to all animals that are not primates? I have a text about the beginnings of brain research, in which the animals studied are divided into "simple animals" (mice, guinea pig, mole, rabbit, reptiles etc.) and "complex mammals and humans" (monkeys, apes, humans). The latter are primates, but I have no idea how to refer to the former group ("simple animals" is so imprecise). I tried on Wiki, but I got completely lost in all those Latin scientific classifications...
Popular imagination, at least in the parts of the English-speaking world with which I can claim some familiarity, does not subdivide the world into primates and non-primates. This is not a traditional distinction— no traditional grouping would have included humans, orangutans, and lemurs in the same collective—and as a scientific categorization, the division is useful only so far as it is for any subdivision of animals: ungulates, annelids, hummingbirds.
Animals which are not primates are simply nonprimates (or non-primates), just as we might add non-ungulates, non-annelids, and non-hummingbirds to the conversation. Biologists may have more specialized terminology, but none that has made its way into popular usage. Nonprimate is certainly a term one can find in primatology journals.
Separate terminology is more common when the distinguishing characteristics are more readily observable than genetic maps, and when the groups are conceptually more equal. Traditional divisions include vertebrate and invertebrate animals and warm-blooded and cold-blooded animals, and more nebulously, the divisions between large and small animals and between higher and lower animals, the boundaries of which no two people will always agree upon.