Removed Sitemap, Search Console errors still there

I recently removed an old sitemap from Search Console because it was full of duplicates and pages that no longer exist – and we already have a new, more up to date sitemap. However when I look at coverage errors in Search Console I’m still seeing all the errors that were caused by the old sitemap. A lot of these are 404s for pages that no longer exist and therefore should not be crawled.

I now know that Search Console doesn’t forget about these errors just because the old sitemap is gone, but how am I supposed to resolve these errors? Will Google keep crawling these error pages even without the old sitemap? And how am I supposed to stop it from crawling 404 pages – it’s not like I can NoIndex or 301 Redirect a page that doesn’t exist!
Help would be greatly appreciated.

Thanks.