There is no way to get a POST param in a single page app, because you cannot POST to a client like a web browser; you can only POST to a server.
See this question.
When you make a POST request, your server interprets the variables and returns a resource (like an HTML page) in response. That page, by default, doesn't have access to any of the headers or data in the request that spawned it. The only reason that you can access GET params is because JavaScript can inspect the URL of the loaded page, which happens to be where the params are stored.
Some server scripting will be necessary, but it shouldn't be too hard. A quick and dirty answer would be to use server scripting to inject the POST params into JavaScript code (for example, in PHP)
echo "<script>doSpecialLogin(".$_POST['superSecretKey'].");</script>"
However, I would also highly recommend that you spend some time making sure that your method is actually secure, and maybe look into technologies like OAuth.