P-type Cu-Se thin films were deposited on glass substrates at room temperature using radio frequency magnetron sputtering by a single multi-component CuSe2 target. When using a multi-component target, the impact of the sputtering power on the homogeneity and stoichiometry within the thin films should be investigated in the depth direction to demonstrate a secondary effect on the electrical and optical properties of the thin films. Systematic characterization of the Cu-Se thin films, including the morphology, microstructure, chemical composition, and depth-directional chemical bonding state and defect structure of the thin films, revealed that the sputtering power played an important role in the homogeneity and stoichiometry of the thin films. At very low and very high sputtering power levels, the Cu-Se thin films exhibited more deviations from stoichiometry, while an optimized sputtering power resulted in more homogenous thin films with improved stoichiometry across the entire thin film thickness in the X-ray photoelectron spectroscopy depth profile, despite showing Se deficiency at all depths. A rapid decrease in carrier concentration, indicating a reduction in the net effect of total defects, was obtained at the optimized sputtering power with less deviation from stoichiometry in the Cu-Se thin films and the closest stoichiometric ratio at an intermediate depth.