A study of photonic bandgap effect and localization in two-dimensional Penrose lattice was performed. Penrose quasicrystals consisted of dielectric rods and defect characteristics of various inequivalent sites of the crystal were investigated. It was observed that the defect characteristics of quasi periodic photonic crystals were different from the periodic case. Localization properties of the defect modes in quasicrystals depended on the position of the removed rod and different defect frequencies could be obtained by removal of rods from various positions.