You could edit your vhost to use a 404 page. Edit a vhost something like this:

server{
    server_name www.foo.com;
    root    /srv/www/foo/public_html;
    expires     1M;
    access_log  /srv/www/foo/logs/access.log;
    error_log   /srv/www/foo/logs/error.log;

    error_page 404 /404.html;

    location / {
        index   index.html;
        rewrite ^/(.*)/$ /$1 permanent;
        try_files "${uri}.html" $uri $uri/ =404;
    }

    location = /404.html {
        internal;
    }       
}

Allright, to customize the nginx template in use for the myapp application, create a file at /home/dokku/<appname>/nginx.conf.template with the default contents.
Edit this file to your needs, so use your custom 404 page error etc.
After your changes a dokku deploy <myapp> will regenerate the /home/dokku/<appname>/nginx.conf file which is then used.

I hope this will work for you

Thanks. My version of dokku is 0.2.3, looks like this functionality was added in 0.3.10. I will update and then try this!

For others who might find this: https://github.com/progrium/dokku/blob/master/docs/nginx.md#customizing-the-nginx-configuration