We studied the inherent limitations of coarse-grained (CG) potentials within the recently developed approach (Kowalczyk et al. J. Phys. Chem. B 2009, 113, 12988-12998). For all studied fluids, the spherically symmetric CG potential constructed according to our scheme modified in this work balances the reproduction of various equilibrium properties (i.e., structural and thermodynamic) measured in CG simulations. The inherent loss of atomistic information at the CG level correlates with the contribution from short-range directional interactions. The highest loss of atomistic information at 298 K and 1 bar is reported for protic liquids (i.e., methanol and acetamide), while the best description at the CG level was obtained for molecular hydrogen and carbon dioxide. The investigated aprotic liquids (i.e., benzene, toluene, and acetone) can be CG into spherically symmetric interaction potentials with some loss of atomistic details. Interestingly, we show that the proposed optimal CG potential reproduces also the interfacial properties of vapor-liquid coexistence for aprotic benzene at 298 K. For all studied fluids, we find that one can easily reproduce structural properties without preserving their cohesive properties or vice versa. However, a general conclusion from our study is the following: an increase in the protic character of a fluid leads to an increase of inherent loss of atomistic details at the CG level.