Disable Comments Feed

I am working on a private site where the comments need to be hidden. I know how to remove the comments feed from the header, but can anyone give me some instructions on how to disable the comments feed altogether. Because all you need to do is add /feed/ to the single post and then you can see the comments feed.

I tried creating feed-atom-comments.php, and feed-rss2-comments.php, and that still did not work.