It’s not possible in wiki text to execute any JavaScript or use even more uncommon HTML. As such you won’t be able to use the MediaWiki API like that.
There are multiple different options you have to achieve something like this though:
You could use the API by including custom JavaScript code on MediaWiki:Common.js
. The code there will be included automatically and can be used to enhance the wiki experience. This obviously requires JavaScript on the client so it might not be the best option; but at least you could use the API directly. You would have to add something to figure out where to place the results correctly though.
A better option would be to use an extension that gives you this output. You can either try to find an extension that already provides this functionality, or write your own that uses the internal MediaWiki API (not the JS one) to access that content.
One extension I could personally recommend you that does this (and many other things), is DynamicPageList (full disclosure: I’m somewhat affiliated with that project). It allows you to perform complex page selections.
For example what you are trying to do is to find all pages which link to your page. This can be easily done by DPL like this:
{{ #dpl: linksto = {{FULLPAGENAME}} }}