Old Subdomain Redirection Issue

We had to take down an old knowledge base type subdomain at my company with thousands of pages (I know). Due to the amount of pages involved, we pointed the entire subdomain to the new knowledge base subdomain.

How do I get the old subdomain to fall out of the SERP? When an old page is found organically and clicked on, it leads to a 404 page with a homepage button that takes you to the new subdomain. I think this is a bad user experience but redirecting on a page by page basis is not an option.

Any insight at all would be much appreciated here.