Add error message on password protected page ONLY when password introduced was incorrect

Try this:

add_filter( 'the_password_form', 'wpse_71284_custom_post_password_msg' );

/**
 * Add a message to the password form.
 *
 * @wp-hook the_password_form
 * @param   string $form
 * @return  string
 */
function wpse_71284_custom_post_password_msg( $form )
{
    // No cookie, the user has not sent anything until now.
    if ( ! isset ( $_COOKIE[ 'wp-postpass_' . COOKIEHASH ] ) )
        return $form;

    // No cookie, person just submitted the form on this page and got the password wrong
    if (wp_get_referer() == get_permalink()) {
      // Translate and escape.
      $msg = esc_html__( 'Sorry, your password is wrong.', 'your_text_domain' );

      // We have a cookie, but it doesn’t match the password.
      $msg = "<p class="custom-password-message">$msg</p>";
    } else {
      $msg = "";
    }
    return $msg . $form;
}