Check out do_shortcode(): http://codex.wordpress.org/Function_Reference/do_shortcode
do_shortcode('[shortcode option1="value1" option2="value2"]');
So your example would be:
do_shortcode('[post_comments]');
What might be easier is to tap into the underlying comment functions:
http://codex.wordpress.org/Function_Reference/comments_number
<p>
This post currently has
<?php comments_number( 'no responses', 'one response', '% responses' ); ?>.
</p>
You can also use get_comments_number
which returns the value rather than printing it to the screen.
This function however needs to be in the Loop for it to work, however I have a feeling it is.