How to acknowledge a more general result?
Cite it as usual. You can note that the paper is an extension of your work. You can, if you feel the need, give the date of the conference, etc. It may be that Y was aware of X from the conference, or it may just be parallel work. 

In any case, your work isn't worthless. Just a symptom, perhaps, of a subfield with a lot of current activity. 

But you should also look at how you and they achieved the respective results. It may be that your, more specialized, paper has proof techniques that are valuable in themselves. There is more to mathematics than the results.