Antikaons in dense nuclear matter are studied using a chiral unitary approach which incorporates the $s$- and p-waves of the $\bar K N$ interaction. We include, in a self-consistent way, Pauli blocking effects, meson self-energies modified by nuclear short-range correlations and baryon binding potentials. We show that the on-shell factorization cannot be applied to evaluate the in-medium corrections to p-wave amplitudes. We also obtain an attractive shift for the $\Lambda$ and $\Sigma$ masses of -30 MeV at saturation density while the $\Sigma^*$ width gets sensibly increased to about 80 MeV. The moderate attraction developed by the antikaon does not support the existence of very deep and narrow bound states.