We study the role of short-range directional interactions in coarse-graining (CG) of protic (i.e., acetamide, methanol, ethanol, and water) and aprotic (i.e., acetone, benzene, and toluene) liquids at normal conditions. For this purpose, we introduce a new CG method in which the average interactions between atomistic molecules and CG beads measured in an N,P,T ensemble are preserved. We show that the spherically symmetric effective CG potential constructed according to our scheme is able to reproduce structural/thermodynamic properties of aprotic liquids; the heat of vaporization and total bonding energy profile for monomer are reproduced with good accuracy, while the density and radial distribution function are reproduced with fair accuracy within the proposed method. In contrast, the isobaric heat capacity is underestimated in the CG simulation because some of the fluctuations have been washed out from atomistic aprotic liquids. For protic liquids, spherically symmetric effective CG potential produces more structure, enhanced packing of beads, and underestimated isobaric heat capacity of CG liquids. This fundamental difference between protic and aprotic liquids can be explained by the presence of short-range directional interactions in the former liquids. We conclude that some information during the CG into spherically symmetric interaction potentials of protic liquids has to be lost, However, understanding how short-range directional interactions influence the structural and thermodynamic properties of the CG liquids seems to be the key for improving the CG methods.