We study numerically the process of vortex nucleation at the wake of a moving object in superfluids using a generalized and non-local Gross-Pitaevskii model. The non-local potential is set to reproduce the roton minimum present in the excitation spectrum of superfluid helium. By applying numerically a Newton-Raphson method we determine the bifurcation diagram for different types of non-linearities and object sizes which allow for determining the corresponding critical velocities. In the case of a non-local potential, we observe that for small object sizes the critical velocity is simply determined by the Landau criterion for superfluidity whereas for large objects there is little difference between all models studied. Finally, we study dynamically in two and three dimensions how rotons and vortices are excited in the non-local model of superfluid.