Password protection for list of posts

I need a section of my website to be password protected from the public. The section I want a password for is just a Page, however, the template for that Page pulls in a list of Posts from a given category. The password is working. The problem is that I can see the Posts without entering a password if I enter the proper URL.

Is there another way of doing this to avoid the security hole?

Btw I’m quite new to WordPress so be gentle.

Thanks,
Ak