You can use the next-error and previous-error commands. By default
next-error is bound to all of C-x [backtick] (note this the x
instead of c), M-g n and M-g M-n; and previous-error is bound
to M-g p and M-g M-p. Out of these my favorites are M-g M-n and
M-g M-p.
By the way, all of those keybindings [1] also work with AucTeX (in
addition to the AucTeX specific C-c [backtick] you mentioned). More
generally, major modes are supposed to arrange for those same commands
to work with whatever kind of "error" messages you might have to deal
with in that mode. I put "error" in quotes because, for example, they
also work with grep or with occur to navigate between occurrences
of the search pattern. Definitely keybindings worth learning!
[1] AucTeX rebinds them to TeX-next-error and TeX-previous-error,
instead of using the standard next-error and previous-error, but
that's just a technicality.