There are a couple of things what you can consider...
You can use one of the available Web Application Firewalls. It usually has set of rules and analytic engine that determine suspicious activities and react accordingly. For example in you case it can automatically block attempts to scan you site as it recognize it as a attack pattern.
More simple (but not 100% solution) approach is check referer url (referer url description in wiki) and if request was originating not from one of you page you rejected it (you probably should create httpmodule for that purpose).
And of cause you want to be sure that you site address all known security issues from OWASP TOP 10 list (OWASP TOP 10). You can find very comprehensive description how to do it for asp.net here (owasp top 10 for .net book in pdf), i also recommend to read the blog of the author of the aforementioned book: http://www.troyhunt.com/