Notify search engines on 404 pages

As suggested in other answers you can handle this issue with help of header status.

If you are still in real hurry and want it removed as fast as possible then you can use remove urls from your Google Webmaster Tools >> Search Console.

Usually it is advisable to allow it to get drop by itself but this is when your 404 page is hurting your rankings or business somehow.

The XML sitemap is usually the best method to pro-actively notify search engines of anything, not just 404 pages. But I fail to understand why you would want to do that? Having 404 pages in Google's index isn't necessarily a bad thing, unless of course these 404 pages are still getting a lot of search hits, in which case you may want to 301 redirect them to some other relevant page. Google usually waits 24 hours before removing a 404 page from its index, but if you want to expedite the process I would suggest returning a 410 status code instead.