You have upgraded to WordPress 3.8.1 properly using your website admin panel.
The problem is that GoDaddy thinks that you should do everything through them rather than you being able to think for yourself.
In the same area where you have been trying to upgrade WordPress through GoDaddy there should be a link that allows you to manually update the version you are using. Just tell their system that you are already using version 3.8.1 and you will be all set.
It’s not necessary to do anything with GoDaddy to keep your WordPress website up to date, but by manually letting them know the version you are using it may stop them from giving you warnings about using out of date software (when you are not).