The role of the crust on the tidal deformability of a cold nonaccreted neutron star is studied using the recent unified equation of state BSk24. This equation of state, which is based on the nuclear energy-density-functional theory, provides a thermodynamically consistent description of all stellar regions. Results obtained with this equation of state are compared to those calculated for a putative neutron star made entirely of homogeneous matter. The presence of the crustal layers is thus found to significantly reduce the Love number k2, especially for low-mass stars. However, this reduction mainly arises from the increase in the stellar radius almost independently of the equation of state. This allows for a simple analytic estimate of k2 for realistic neutron stars using the equation of state of homogeneous matter only.