Best practice for acceptance test handling?

I'm not sure if there even is an answer, but I'm asking anyway:

In my company I'm the only one in charge of the software testing, which is currently done (mostly) manually. We partially start to automate tests and encountered a question in organisation here. In my development team (consists of 5 people) the following question popped up:

Is there any way to see which acceptance criteria of an user story are tested, and by which tests?

I know that I can link the test case to the user story within the Team-Foundation-Server. But there is no direct way to tell which test tests which acceptance criteria.

I would be glad if any of you can be of help to me here - I'm a newbie in software testing, and do everything just with best intend (no certifications so far)

Thank you, Frank