Latest posts list: Exclude posts with certain tags

Currently I’m able to pull the latest two posts onto my static front page like this…

<?php
$args = array( 'numberposts' => 2, 'order'=> 'DESC', 'orderby' => 'post_date' );
$postslist = get_posts( $args );

foreach ($postslist as $post) :  setup_postdata($post); ?>
  <p>
    <?php the_time('F j, Y'); ?>
  </p>
  <h5>
    <a href="<?php echo get_permalink(); ?>">
      <?php the_title(); ?>
    </a>
  </h5>
  <div>
    <?php the_excerpt(); ?>
  </div>
<?php endforeach;

?>

That all works well – it displays the date, title link, excerpt and More link for the latest two posts.

However, I’m looking for a way to prevent any posts that have been tagged with the word ‘exclude’ from displaying in this area. Does anyone know if there is a way to tweak the above code to accommodate that? Or is there a better way of achieving it?

(I’ve been playing around with tag__not_in but that seems to be something to do with WP_Query and I can’t work out how to incorporate it.)

Any help would be greatly appreciated.