I have many pages from one year ago that were deleted and are returning a 404 error code, but two week ago after I cleared the content of my robots.txt, the errors in my Google Webmaster Tools reports are still showing them as not found.After I read this Google support document, today I inserted these new meta tags for 404 error pages:<meta name=robots content=noindex><meta name=googlebot content=noindex> and after added that,  I decided to change the header from: header(HTTP/1.0 404 Not Found);  to header(HTTP/1.0 410 Gone);Do you think these new changes are right?
Did I use the proper way to remove pages from Google Webmaster Tools forever?
google search console;404;meta tags;http headers;410 gone
It is a common mistake that people worry about 404 errors found in Google Webmasters Tool for pages that do not exist. This is a natural functioning of a website and search engine and therefore nothing to fix. If the page is gone, then a 404 error is appropriate.What frustrates people in these cases is that they feel that Google is still trying to access these pages after they have clearly been deleted. The most common reason for this is that Google found a link to that page somewhere on the web and placed it in the fetch queue. There is nothing you can do about that. That is normal functioning.If the page is truly gone, then do not worry about the error. Google will retry the page several times before giving up. But it may try and visit the page again later because of any link found. Do not worry about it. You do not have to use robots.txt to exclude the page, however, there is no harm in this except that Google will not know the page does not exist. Under no circumstances should you mark a proper 404 error as having been fixed in Google Webmasters Tool. This is akin to telling Google that the page should be found and to keep trying.To answer the question in your title: You cannot tell a search engine that a page does not exist other than a 404 or 410 error. There is no SEO downside to this. None at all.