A quick and dirty would be to set up a 301 from admin.sitename.com/index.php to admin.sitename.com/ unless you are using a CMS which may cause problems. Also, I use cPanel, and I can password protect through the interface. my .htaccess file ended up looking like
However, it is puzzling to me why <Files ''> works at all; The <Files> and <FilesMatch> directives apply to files, not URLs. Further, they apply to files in the current directory and in any subdirectories of this directory -- that is to say that the filename will be matched regardless of sub-directory path. And since you cannot have a blank-named file in the server filesystem, I don't know how <Files ''> can work at all.
Because of that, I also don't know how my <FilesMatch> suggestion could work, because technically it should not.
So all-in-all, I prefer youfoundjake's suggestion, as it eliminates this "mystery mode."