Having just started trying out zsh, I ran into this problem too. You can do setopt interactivecomments to activate the bash-style comments.
The Z Shell Manual indicates that while this is default behavior for ksh (Korn shell) and sh (Bourne shell), and I am guessing also for bash (Bourne-again shell), it is not default for zsh (Z shell):
In the following list, options set by default in all emulations are marked
<D>; those set by default only in csh, ksh, sh, or zsh emulations are marked<C>,<K>,<S>,<Z>as appropriate.
INTERACTIVE_COMMENTS (-k)
<K><S>
Allow comments even in interactive shells.