The zero K formation energies of metal and nitrogen vacancies in several (Ti,Al)N alloys and at the (001) (Ti,Al)N/AlN interface are obtained in ab initio supercell calculations. The dependence of the formation energies of metal vacancies on their local environment and type are analyzed and explained in terms of effective cluster interactions for unrelaxed calculations. The common trend for all investigated types of vacancies is that their formation energy increases with the number of Al nearest neighbors if local lattice relaxations are not allowed. However, local lattice relaxations produce a dramatic effect especially in the case of metal vacancies leading to a complicated nonlinear dependence on the local environment indicating the existence of strong multisite strain-induced interactions.