Well, according to https://technet.microsoft.com/en-us/library/jj863434(v=exchg.150).aspx you can not.
|Archive mailbox||Yes||No *|
|Resource mailbox (Room or Equipment)||No||Yes|
If you use PowerShell, you most definitely can!
PS C:\temp> get-mailbox TestRoom |FL *rec*
RecipientType : UserMailbox
RecipientTypeDetails : RoomMailbox
PS C:\temp> Disable-Mailbox TestRoom
Are you sure you want to perform this action?
Disabling mailbox “TestRoom” will remove the Exchange properties from the Active Directory user object and mark the
mailbox in the database for removal. If the mailbox has an archive or remote archive, the archive will also be marked
for removal. In the case of remote archives, this action is permanent. You can’t reconnect this user to the remote
[Y] Yes [A] Yes to All [N] No [L] No to All [?] Help (default is “Y”): Y
What you can not do is disable a resource mailbox via EAC. The disable option simply isn’t there for some reason. Seems like an odd oversight.