We numerically investigate the quMity factors of two-dimensionM (2D) photonic crystal (PC) microcavities using an auxiliary differential equations (ADE) technique in the context of finite-difference time-domain (FDTD)method. The microcavities are formed by point defects in the air hole lattice hexagonedly patteed in ZnO (zinc oxide) matrix. The quality factors of these microcavities are limited primarily by the absorption of the background dielectric. We show that the ratio between the quality factors of microcavities in lossy and lossless background dielectric depends on the overlap between the field of cavity modes and the absorbing background dielectric in addition to the magnitude of absorption. These results will be helpful when designing and optimizing photonie erystal microcavities formed in lossy medium.