When in Grid and you display attributes such as Star ratings (no filter applied), do you see the 1-star attribute attached to your images? Provided you do, you should certainly be able to display only 1-Star images. Common problems are:
1) The folder or collection you are filtering, meaning the library left panel asset you are selecting has no images containing the filter you've imposed. This would mean for you that you are searching a folder or collection containing no 1-Star images, hence no images show.
2) You've imposed, without meaning to, a filter in addition to the filter you want - in your case 1-star rating. The easiest filter to activate without recognizing it is the Flag/Unflagged status (left group of filter buttons). So an example would be that your Filter bar has engaged 1-star (as intended), but also Flagged images (not intended). Other unintended filters could include color filters, and text string filters (at the top of the grid window).
So first assure that you have in fact attached the 1-star attribute by examining your images within Grid (without any filters imposed), and then be sure that you have invoked the intended, and only the intended, filters. This aspect of LR works very well, in my mind. You should be OK once you get the hang of it.
John Caldwell