Highlight current post type when inside custom post type

I am assuming that your code is on a “single” post/cpt page.

echo '<ul>';
  $loop = new WP_Query( array( 'post_type' => 'post', 'posts_per_page' => 4, 'order'=>'ASC' ) );
  $obj = get_queried_object();
  $thispage = $obj->ID;
  while ( $loop->have_posts() ) : $loop->the_post(); ?>
    <li><?php 
      if ($thispage === $post->ID) {
        $class=" class="current-item"";
      } else {
        $class="";
      }
      the_title( 
        '<a href="' . get_permalink() . '" title="' . the_title_attribute( 'echo=0' ). '"' . $class.' >', 
        '</a>' 
      ); ?>
    </li><?php 
  endwhile;
echo '</ul>';

You want to use get_queried_object to get data about the page you are on and compare the ID to the items in the loop, adding a class attribute if they match. This will not work correctly on archive pages as get_queried_object will not return the same type of data on those pages. Depending on your implementation, you may have to alter the code.