How to Stop Old invalid links/bookmarks hitting the new website?

I have a heavy traffic website, where i recently upgraded the whole website to new system, where most old urls are now not valid and causing problems in the new system. Most of the old urls are saved in the users browsing history.

How do i make sure these old links/bookmarks are redirected to the main page of the new website

please note i am using nginx and its not possible to redirect by one by one as website is large and not possible to do them manually.

Any ideas ?