Am I responsible for that my PhD adviser does not have any fund or grant and as a result it really limited my research?
In general, this is bad form on the part of the advisor and your committee (shouldn't be approving thesis topics that are not viable if funding is not available). As a PhD student, you are in training and potential stumbling blocks should be made clear to you. 

For example, for my PhD I worked in a lab where I wanted to do field work in another country, but my advisor didn't have funding for this. I decided to go ahead with this part of the project, partially using my own personal funds, as well as cobbling together several small research grants to cover these costs.

So I would recommend to you that you investigate research funds that might be available from your department, institution, scientific society, foundation, or other non-federal source. Funding begets funding and you absolutely have to be successful in getting grants to be a successful academic. 

Additionally, it seems odd that an advisor could take on a student with no funding in the lab. That would not be allowed in my department (biology sub-field at a private, R1 university). 

Finally, to your last question: I think you are correct and it is unreasonable to compare the contribution of a single graduate student with "famous" well-funded labs! The contribution to your field during your PhD can be modest- that's ok- but it has to be good science, so I would focus on how to make sure that you are doing the most rigorous and sound research with the resources you have available. And get to writing grant applications! Good luck.