The Curie temperature of diluted (Ga,Mn)As magnetic semiconductors in the presence of As antisites is studied from first principles. We map total energies associated with rotations of Mn-magnetic moments onto the effective classical Heisenberg Hamiltonian which is treated in the mean-field approximation to find the Curie temperature. The presence of donors strongly reduces the Curie temperature and gives rise to a ground state with a partial disorder of local moments. We show that the observed dependence of the Curie temperature on the Mn concentration indicates that the concentration of As antisites increases with the Mn content.