The steel vessels of pressurized water reactors are embrittled by neutron irradiation. It is well known that copper atoms play an important role in the embrittlement and that different Cu- containing defects such as Cu-rich clusters (sometimes called atmospheres), Cu precipitates and Cu-vacancy complexes have been identified experimentally. It is still difficult to link the formation of these defects to the primary damage resulting from the neutron inducing displacement cascades. Therefore, we investigate the evolution of the primary damage in FeCu alloys using kinetic Monte Carlo simulations based on a vacancy diffusion mechanism. The calculations rely on adapted, phenomenological, n-body potentials that satisfactorily reproduce properties of FeCu. At room temperature, experimentally identified defects such as Cu-vacancy complexes (one Cu atom bound to three or four vacancies) form in the course of our simulations. Furthermore, it appears that complex defects such as a Cu atom linked to two vacancies are very mobile and are responsible for the formation of small Cu clusters.