Add a function call after content automatically?

You’ve already been pointed to the correct approach and the answer is functionally identical to any of the answers here about appending data to post content. All you need is something like:

function my_function () {
  echo 'my function content';
}
add_action('the_content','my_function');

To restrict that to single post pages:

function my_function () {
  if (is_single()) {
    echo 'my function content';
  }
}
add_action('the_content','my_function');