Next and Previous Links for Posts on Page not Working

I have made a custom plugin which displays recent N posts from several categories on a static page. The posts are queried with WP_Query(cat=1,2,3) with subsequent loop for displaying the posts.
And the problem is that I cannot get next_posts_link() and previous_posts_link() functions work for my posts.
Is there a workaround or a hack for solving this problem?
Thank you.