Coarse-grained models are becoming increasingly popular due to their ability to access time and length scales that are prohibitively expensive with atomistic models. However, as a result of decreasing the degrees of freedom, coarse-grained models often have diminished accuracy, representability, and transferability compared with their finer grained counterparts. Uncertainty quantification (UQ) can help alleviate this challenge by providing an efficient and accurate method to evaluate the effect of model parameters on the properties of the system. This method is useful in finding parameter sets that fit the model to several experimental properties simultaneously. In this work we use UQ as a tool for the evaluation and optimization of a coarse-grained model. We efficiently sample the five-dimensional parameter space of the coarse-grained monatomic water (mW) model to determine what parameter sets best reproduce experimental thermodynamic, structural and dynamical properties of water. Generalized polynomial chaos (gPC) was used to reconstruct the analytical surfaces of density, enthalpy of vaporization, radial and angular distribution functions, and diffusivity of liquid water as a function of the input parameters. With these surfaces, we evaluated the sensitivity of these properties to perturbations of the model input parameters and the accuracy and representability of the coarse-grained models. In particular, we investigated what is the optimum length scale of the water-water interactions needed to reproduce the properties of liquid water with a monatomic model with two- and three-body interactions. We found that there is an optimum cutoff length of 4.3 Å, barely longer than the size of the first neighbor shell in water. As cutoffs deviate from this optimum value, the ability of the model to simultaneously reproduce the structure and thermodynamics is severely diminished.