Follow up while the postings imply not to follow up?

I applied for a couple of jobs approximately 1.5 months ago. Both postings say only qualified candidates will be contacted. I have not heard from them yet and I was wondering should I follow up with HR regarding the application (or ask where can I improve to apply for future opportunities).

FYI, I am not really qualified for both jobs with respect to the experience requirement (1-2 years of IB experience). However, I have seen people getting the same positions straight from undergrad or after 2-3 years in big 4. Therefore, I don't think lacking of IB experience is a definite no. I have 2 years of experience in finance, and I have pretty much the same responsibilities and and duties at my current jobs, just in different industry though (real estate acquisition vs project finance).