Yes you can.
Open the index.php file of the theme and find the string given below
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
Now right below that string use this code
<?php if (in_category('25,15,13')) continue; ?>
Now you need to understand that the numbers 25,15, 13 are just dummy numbers I used in the code. They actually represent the category id of the category you want to exclude. So in your case you will have to find the cat-id for those categories you want to exclude from your admin panel. You need to insert those numbers in the above code.
This will exclude posts from those categories from the blog page.
But however there is a downside for this. That is, the blog will display a blank space where the excluded post was supposed to be located. I am still unable to find a workaround for this.
Hope that helps
Jinsona