We have recently achieved a non-dispersive, low-order pseudogap in the blue region near the L-point in electrodeposited ZnO inverse opal. This behavior is a consequence of the change in the interconnecting network of interstices from a low dielectric (air) in the opal to a high dielectric one in the inverse opal. To verify this, we present the calculated photonic bands along the LW direction, which corresponds to the angular range explored experimentally by means of angle-resolved spectroscopy. We also studied the dispersion as a function of refractive index contrast (RIC). Further increase of the RIC above the threshold necessary to open up a complete photonic bandgap between the 8th and 9th bands does not have significant effects on improving the non-dispersive characteristic in the pseudogap. The results could be extended to make other inverse photonic structures of different symmetry with non-dispersive bands suitable for the study of optical processes involving low group velocity.