A sitemap may help with indexing your new URL structure, but remember Google makes no promises they'll crawl or index everything in there at all.
However, even if they did index everything in your sitemap, that would not magically make your crawl errors go away. 404(not found) errors explicitly allow for the possibility that the URL may be available again in the future, eg. your site was temporarily down. Google will continue to try these URLs for some unspecified amount of time and eventually drop them if the 404 persists. You don't have to do anything, but you can help the process along a bit:
As much as is possible, you should arrange 301 redirects for any content that did get migrated. This will explicitly inform Google that the old URL for Document X is bad and should be updated to the new one. To explicitly tell crawlers that a document is gone forever, you should send a 410 response.