How to get post or page excerpt using post_excerpt

EDIT

Seems that I some how misunderstood you. I do think you are missing the point of the post_excerpt.

When you create a new post or page (AFAIK for pages as well), you have the opportunity to create a manual excerpt in the excerpt meta box (to make it available, just enable it in screen options dropdown when in the add new/edit post/page screen). This manual excerpt (or user defined excerpt) that you enter in that meta box is saved under post_excerpt, which you can then retrieve with $post->post_excerpt. If that meta box is empty, ie, if you haven’t specified a manual excerpt, nothing will be returned

It does not work the same as the template tag, the_excerpt() that creates an excerpt on the fly by using the content to create an excerpt, which BTW doesn’t work on pages.

Please check out WP_Post

post_excerpt

string

User-defined post excerpt

EDIT 2

If the manual excerpt meta box is not displayed, you can simply activate it with the following code

add_action( 'init', 'add_excerpts_to_pages' );
function add_excerpts_to_pages() {
     add_post_type_support( 'page', 'excerpt' );
}

ORIGINAL ANSWER

Your usage of get_pages here is wrong here. get_pages is not intended for this use.

You should be using a custom query with either get_posts or WP_Query

You can do something like this to display your pages and excerpts

<?php

// The Query
$the_query = new WP_Query('post_type=page' );

// The Loop
if ( $the_query->have_posts() ) {
  while ( $the_query->have_posts() ) {
    $the_query->the_post();
       the_title();
       the_excerpt();
    }
  } else {
  // no posts found
}
/* Restore original Post Data */
wp_reset_postdata();