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You've also lost all the value of inbound links to content pages (meaning, everything except the homepage) on the old site. I would recommend you pull a list of inbound links from your old server logs or from Google's webmaster console (see the "links" tool and download the .csv file) and have your IT department create 301 redirects from all the important .html pages to their new .asp pages. This will help retain the link juice accumulated by the old site.
Or, if it is true that every old foo.html page has an equivalent with the new extension (foo.asp), then create a blanket 301 redirect within your 404 handler, such that a request for anything.html results in a 301 to anything.asp. That's easier than creating many individual redirects.
The takeaway lesson here (IMO) is, never change all your URLs. I know Apache can be configured to use any file extension. I suspect the same is true for Microsoft server products. There's just no reason to erase years of accumulated authority/link juice/etc due to a server-software configuration issue!
Whether or not this makes sense to you, it should be pretty clear to the folks who either created the site or who maintain the server. If your CMS consultants can't help with this, they really shouldn't be in business -- it's hardly good service to rob their clients of all their search-engine rankings (IMO).
The .asp extension signifies that an ASP script sent the HTML out to the browser. What that extension is, does not matter to a browser. It could be .xyz or .abc for all it cares... but a change of extension is a change of URL.
I have a site where all the URLs end in .asp but the content is actually pushed out by a PHP script. Bots and browsers don't care what made that page, it is all internal to the server. All they care about is that the content arrives flagged as "text/html" with a "200 OK" status in the HTTP header.
How long has the new site been live? If it were only a few days, I would get all the URLs changed back to the old ones, immediately. If it has been too long, or is just too difficult, then you absolutely need a 301 redirect from each old URL to each new URL. This allows visitors following old links to still arrive at the correct page of your site, and tells search engines to update their listings.
Here is how we tackled it recently for someone using Apache and who mistakenly changed all his URLs from .html to .php - [webmasterworld.com...]