We report x-ray powder diffraction and temperature-dependent infrared reflectivity measurements of (Na(0.5)La(0.5))Cu(3)Ti(4)O(12) and (Na(0.5)Bi(0.5))Cu(3)Ti(4)O(12) in order to investigate the origin of their lower room-temperature dielectric constants in comparison with the giant value of CaCu(3)Ti(4)O(12). Substituting Ca with Na/La or Na/Bi is found to decrease all Ti-O-Ti angles by the TiO(6) octahedra tilts, resulting in an increase of the local structural disorder on the Na/La and Na/Bi compounds. Further, several infrared-active phonon modes show a broadening in their linewidths, reflecting that the coherency in these vibrational modes is degraded by disorder. Additionally, the lowest-frequency mode of the Ca material is observed to strengthen dramatically at low temperatures, but to a lesser extent in the Na/La and Na/Bi compounds. These results suggest the important role of the local structural disorder on the anomalous low-frequency dielectric response in these materials.