Should I mention I had no funding in my Ph.D experience? A professor mentioned on his website that his looking for postdoctoral researchers. And he mentioned that interested people should sent a short research statement and added this link.


Discuss where you will get funds to sponsor the research project, who will be the collaborative partners and what facilities will be used by you.


Unfortunately, I did research under no funding because it's hard to find research grants in my country. And it's not mandatory to have a grant or a scholarship to be a Ph.D student. But that's another topic. Now, I am trying to write a research statement and I don't know if I should completely ignore talking about funding. The only thing I have is experience in preparing, with my supervisor, project proposal documents for funding (Around 2 months of work). I don't know if I should write that, because it also could be a double-edged sword since my experience is "failure in finding funding". Any suggestions?
I can't see into the mind of the PI, but think that you would harm your chances by suggesting that you might not need funding when they may be, explicitly, looking for funding sources. (Caveat below)

Since they ask for your proposed funding sponsors, you probably need to provide that to be in contention. If you can do that then an "Oh by the way, I've done research without funding" may not hurt you, but otherwise it could (possibly). 

But you would probably be wise to look elsewhere for a PI that can themselves provide funding for their postdocs. If they can't do that, I wonder how much commitment they will have to you. 

Of course, since the link is a very general one, they may not require all elements, especially self funding. You could also inquire directly about that.