In Tridion 2013 we are getting generic exception for the pages that do not exist in the website. Is there a way to prevent generic errors due to invalid page requests? Thanks.
You cannot prevent an exception or error being thrown by the application for pages or items that does not exist. However, you can customize the error message or throw errors differently to create a better user experience.
You can look through the example for DXA 1.4. It should be pretty similar to the DXA version that you are using, though.
The other way would be to change the default ServerError.jsp in your web application. This would change the default error message from DXA though.