I just tried this and it works for me.
Given that you would like to exclude page id 4 this is the code you are looking for.
<?php
$pagelist = get_pages('sort_column=menu_order&sort_order=asc&exclude=4');
$pages = array();
foreach ($pagelist as $page) {
$pages[] += $page->ID;
}
$current = array_search($post->ID, $pages);
$prevID = $pages[$current-1];
$nextID = $pages[$current+1];
?>
<div class="navigation">
<?php if (!empty($prevID)) { ?>
<div class="alignleft">
<a href="https://wordpress.stackexchange.com/questions/78706/<?php echo get_permalink($prevID); ?>"
title="<?php echo get_the_title($prevID); ?>">Previous</a>
</div>
<?php }
if (!empty($nextID)) { ?>
<div class="alignright">
<a href="<?php echo get_permalink($nextID); ?>"
title="<?php echo get_the_title($nextID); ?>">Next</a>
</div>
<?php } ?>
</div>