Recently published paper does not cite my very relevant work
That happens. Maybe they didn't do a thorough literature study before they published, or they did but before your work was available. This is more frequent than we would like to think. Note that it's generally expected from authors to have done a reasonable effort in searching for previous work, but it's not unethical per se not to reference every previous publication that could be relevant (it's also practically very hard).


  Is there anything I can do regarding that already-published paper?


No, missing a previous related work is not a valid motivation to complain to the authors or editors. Just forget about it and move on. 


  Is there anything I can do to prevent this from happening in the future?


Yes, become so influential in your field that reviewers will know your work enough to spot when someone else submit a related work without citing yours.

Side note:


  I am keen on improving my h-index and citations count.


Without going into how this might not be what you should focus on (while very good researchers tend to have a high citation count, the inverse relation is not always true), the best way to do that is to produce high-quality research, preferably on a hot research topic.