Applying for internships and looking for jobs is very similar to the college application process in my opinion, except there are more applications and generally more rejection. I applied to 37 companies during the first semester of my junior year and received 10 interviews, and ultimately 3 offers. That's a lot of rejection! Ultimately, the only thing that I cared about was that I had any offers at the end of the day and understanding that fewer than a third of companies wanted me to interview with them, but I still had an offer to go to.
This is the most difficult part of the search process. I think that with more and more interviewing experience, people will become more confident and understand how the process works. In order to get that experience however, there will be rejection. There is no way to gain experience without having some failures.
It's hard to deal with rejection! I would try to arrange a phone call with your recruiter to discuss specifics on where you may have faltered in the process. Be honest and responsive to the feedback they provide you! There are any number of reasons for a rejection, but showing you're willing to improve and grow from this experience allows you to be better prepared for future applications.