We have determined from first principles the Curie temperature in a diluted magnetic semiconductor (Ga_1−x−yMn_xAs_y)As alloys, where the compensation effect by As antisites is taken into account. The disorder due to random positions of Mn impurities and As antisites is taken into account in the framework of the coherent potential approximation. We demonstrate that a simple mean-field approximation (MFA) already gets T_C accurately. In particular, it is shown that the calculated T_C in the random-phase-approximation and Monte Carlo simulations differ only weakly from the MFA values. The reason is that a proper treatment of the disorder beyond the virtual-crystal approximation leads, in this doped material, to a flat magnon dispersion in a large part of the Brillouin zone.