We have computed the entropy of liquid water using a two-phase thermodynamic model and trajectories generated by ab initio molecular dynamics simulations. We present the results obtained with semilocal, hybrid, and van der Waals density functionals. We show that in all cases, at the experimental equilibrium density and at temperatures in the vicinity of 300 K, the computed entropies are underestimated, with respect to experiment, and the liquid exhibits a degree of tetrahedral order higher than in experiments. The underestimate is more severe for the PBE and PBE0 functionals than for several van der Waals functionals.