Although Dancer (and most of these other frameworks, including Catalyst and Mojolicious) comes with a mini-webserver bundled into the framework, it's really only intended for development purposes, so that you can debug your app in a persistent environment without having to restart apache every time you modify the code. This HTTP server is not intended to be used in production deployments.
For production purposes, the app would normally be mounted under a specific base URI in apache (or starman or whatever your preferred web server might be) and any requests falling under that URI get passed off by apache to Dancer, just like they would for a bare-bones script running under CGI, FastCGI, PSGI, mod_perl, or whatever. Dancer would not normally be running as a server itself.
(If you really wanted to, I guess you could run Dancer as its own HTTP server on another port and have apache proxy requests to that port, but that would add unnecessary complexity and is neither the standard nor the intended way of doing it.)