Sweetie, I'm sorry to hear that!!

Rejection sucks, no matter what it is.
I believe that we must find a good match with a job. I remember that after I graduated (even before) I was aiming for a job at a specific psychiatric hospital. I applied, never heard from them, contacted them and they said they lost my app. So I filled out another one, interviewed the same day, and never heard back from them again. I considered them the best psych hospital in the area, and I was upset. However, after getting a job at another psych hospital, I heard from former employees how bad the work environment is there. Disorganization (hence the lost app!), low respect for employees, little teamwork. . .I realized I wouldn't be happy there. I'm glad I got the job I did.
Use this as a learning experience. If it would make you feel better, contact them back and ask them what you need to work on, why you were not a good fit, etc. But be prepared for some hard answers to that question, and don't get upset!!! Let yourself feel bad for a day, then pick up and move on. Look around for another job/internship. . .you will find one!!
Tau Love,
PsychTau