In embedding methods such as those labeled commonly as QM/MM, the embedding operator is frequently approximated by the electrostatic potential generated by nuclei and electrons in the environment. Such approximation is especially useful in studies of the potential energy surface of embedded species. The effect on energy of neglecting the non-Coulombic component of the embedding operator is corrected a posteriori. The present work investigates applicability of such approximation in evaluation of electronic excitation energy, the accuracy of which depends directly on that of the embedding potential. For several model systems involving cis-7-hydroxiquinoline hydrogen-bonded to small molecules, we demonstrate that such truncation of the embedding operator leads to numerically unstable results upon increasing the size of the atomic basis sets. Approximating the non-Coulombic component of the embedding potential using the expression derived in Frozen-Density Embedding Theory ([Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050] and subsequent works) by means of even a simple bifunctional dependent on the electron density of the chromophore and its hydrogen-bonded environment, restores the numerical stability of the excitation energies that reach a physically meaningful limit for large basis sets.