A theoretical model of a two-component bilayer membrane was used in order to describe the influence of anisotropic membrane inclusions on shapes of membrane daughter micro and nano vesicles. It was shown that for weakly anisotropic inclusions the stable vesicle shapes are only slightly out-of-round. In contrast, for strongly anisotropic inclusions the stable vesicle shapes may significantly differ from spheres, i.e. they have a flattened oblate shape at small numbers of inclusions in the membrane, and an elongated cigar-like prolate shape at high numbers of inclusions in the vesicle membrane.