  Inclusive production of $J/\psi$ mesons, especially at forward rapidities, is
an important probe of small-x gluons in protons and nuclei. In this paper we
re-evaluate the production cross sections in the Color Glass Condensate
framework, where the process is described by a large x gluon from the probe
splitting into a quark pair and eikonally interacting with the target proton or
nucleus. Using a standard collinear gluon distribution for the probe and an up
to date dipole cross section fitted to HERA data to describe the target we
achieve a rather good description of the cross section in proton-proton
collisions, although with a rather large normalization uncertainty. More
importantly, we show that generalizing the dipole cross section to nuclei in
the Glauber approach results in a nuclear suppression of $J/\psi$ production
that is much closer to the experimental data than claimed in previous
literature.
