Playing very softly while avoiding ghost notes is a fairly difficult and common technical issue that requires practice. It can be exacerbated if the piano's regulation is in bad shape but I will only discuss the technical approach to solving this problem. Just like any technical issue, just practicing it over and over with a hope that the problem will eventually be solved is not nearly as good as having a clear idea about how to solve the problem. I think by far the best explanation of how to play softly while avoiding ghost notes is the one in the following video by Denis Zhdanov:
Although I recommend watching the whole video here is a short summary. Play with firm fingers to the bottom of the key and achieve pp sound by depressing the key slowly. Don't think of playing lightly on the keys or with less than firm fingers or just pushing the keys partially down. He explains everything much better than I can.