I've seen quite a few posts on this issue, but all point to using a remove_action function to remove the RSS links. This may work, depending on your setup. But, considering that many users are probably customizing the default Twenty* WordPress theme, the process is both different and simpler.
Within your functions.php, simply comment out the line:
// add_theme_support( 'automatic-feed-links' );
Now, as other posts suggest, you do need to add back the post feed.
<link rel="alternate" type="application/rss+xml" title="<?php bloginfo('name'); ?> RSS Feed" href="<?php bloginfo('rss2_url'); ?>" />
This post was actually conceived by the fact that the comments RSS link actually produced a 404 error, so it's certainly a good idea to remove it if that's the case for your blog.