Then it sounds to me you have to setup Internet Explorer or Firefox to use the user and password for the proxy to connect to your adminpage/fireplay on port 3689.
Doing a quick search in Firefox I found a way to do the same as winamp:
Tools -> Options -> Advanced -> Network (tab) -> Settings
But I’m not sure if the proxy will work, as you will be connecting to port 3689.
Maybe this addon might help you out.
(I hope you’re using firefox XD)