Protozoa are animal-like, one-celled animals, such as amoebas. Some are parasites that cause infections in the body. African sleeping sickness, giardiasis, amebiasis, Pneumocystis carinii pneumonia (PCP), and malaria are examples of diseases caused by protozoa.rotozoa are animal-like, one-celled animals, such as amoebas. Some are parasites that cause infections in the body. African sleeping sickness, giardiasis, amebiasis, Pneumocystis carinii pneumonia (PCP), and malaria are examples of diseases caused by protozoa.