display only parent replies count in index.php

Based on this answer I suggest the following code:

// the theme's functions.php

/**
 * Get the number of top level comments for a post.
 *
 * @param  int $post_id
 * @return int
 */
function wpse_95242_top_level_comments_for_post( $post_id = NULL )
{
    if ( NULL === $post_id )
        $post_id = get_the_ID();

    if ( ! $post_id )
        return 0;

    add_filter( 'comments_clauses', 'wpse_95242_where_top_comments_only' );

    $comments = get_comments(
        array (
            'post_id' => $post_id
        )
    );

    remove_filter( 'comments_clauses', 'wpse_95242_where_top_comments_only' );

    if ( ! $comments )
        return 0;

    return count( $comments );
}

/**
 * Filter comment query for top level comments.
 *
 * @wp-hook comments_clauses
 * @param   array $clauses
 * @return  array
 */
function wpse_95242_where_top_comments_only( $clauses )
{
    $clauses['where'] .= ' AND comment_parent = 0';
    return $clauses;
}

In your loop you call the function on each item:

printf(
    __( '%d top level comments', 'theme_text_domain' ),
    wpse_95242_top_level_comments_for_post()
);