You can use the ^(pattern1|pattern2|...) syntax to match everything except the given patterns in zsh.

First you have to enable extended globbing, using setopt extended_glob. For example:

touch foo; touch bar; touch baz

setopt extended_glob # this is needed for the pattern to work
echo ^(foo|bar) # outputs "baz"
The case with a single name is a little bit counterintuitive, because the “” symbol is mandatory:
echo ^(bar|) # outputs "baz foo"

You can complicate the pattern further:

echo ^(ba*|) # outputs "foo"

Thank you, Super User!