Unfortunately, you cannot. The Everyone group is one of those "special" Windows NT 4.0 groups. Other special groups include: Creator Owner, System, Interactive and Network. Here are the details on each group:
Everyone - Anyone using the computer. This includes all local and remote users (that is, the Interactive and Network groups combined). In a domain, members of Everyone can by default access the network, connect to a server's shared network directories and print to a server's printers.
Creator Owner - The creator of the object such as a print job, file or folder
Interactive - Anyone using the computer locally.
Network - Anyone using the computer over a network
System - The operating system
These special groups are created by the system and memberships to these groups cannot be altered. You will also notice that these groups are not listed in the User Manager for Domains. They are visible when you are assigning permissions to directories, files, shared network directories or printers.