The ability of red blood cells (RBCs, erythrocytes) to deform and pass through capillaries is essential for continual flow of blood in the microvasculature, which ensures an adequate supply of oxygen and nutrients, prompt removal of metabolic waste products, transport of drugs and hormones, and traffic of circulating cells to and from all living tissues. This paper presents a novel tool for evaluating the impact of impaired deformability of RBCs on the flow of blood in the microvasculature by directly measuring perfusion of a test microchannel network with dimensions and topology similar to the real microcirculation. The measurement of microchannel network perfusion is compared with RBC filtration -- a conventional assay of RBC deformability. In contrast to RBC filterability, network perfusion depends linearly on RBC deformability modulated by graded exposure to glutaraldehyde, showing a higher sensitivity to small changes of deformability. The direct measurement of microchannel network perfusion represents a new concept for the field of blood rheology and should prove beneficial for basic science and clinical applications.