Discovering 404s can be useful.
Is the old page deleted? Why not 301 redirect the URL to an appropriate page elsewhere on your site? Tools such as Screaming Frog's SEO Spider can crawl your website and help you discover 404s. By redirecting the page with a permanent redirect search engines will to pass any link juice the previous page had to the new page. Redirecting will also cleanup your pages in the SERPs and help with any broken internal links on your site (though it'd be better to fix those).
There's no need to having a rel=canonical tag on a 404 page (but if you do, ensure the tag is for the page itself and not actual content on your site).
There's also no need for search engines to index your 404 page, so I suggest adding the meta NOINDEX tag to the page.