Recent Posts Listed by Author, Can I exclude authors?

You could try the following SQL query:

"SELECT DISTINCT post_author FROM $wpdb->posts WHERE post_author NOT IN (1,3,4)"

to exclude authors 1,3 and 4.

In general it would be more handy to retrieve the user ids automatically, so you wouldn’t need to update your SQL query every time you want to exclude someone.

You could for example use the user meta to label those users that you want to exclude.