Google Chromecast, as well as newer versions of Android, are forced to use Google's DNS servers. This means that if you are using a DNS redirection service to access Netflix for example, it will not work on the Chromecast or on your Android device.
This tutorial takes a little bit of technical know how, and you may have to use Google to find the exact procedure for your specific brand of router.
Step 1: Enable the DNS service on your home router
Step 2: Configure your home router to use your DNS redirect service as it's own DNS server
Step 3: Configure your home router to issue DHCP, with it's own internal IP as the DNS server
Step 4: Add the following IP addresses to your router as IP Aliases:
Step 5: Reboot your network router and wireless access point