How can I filter posts by post_parent in the admin?

The problem is that ‘post_parent’ is not a public query var, i.e. you can use it only from code.

To be able to use it from the URL, you just need to add these lines of code:

function make_post_parent_public_qv() {
    if ( is_admin() )
        $GLOBALS['wp']->add_query_var( 'post_parent' );
}
add_action( 'init', 'make_post_parent_public_qv' );