I got an interview with the company that would become my first dispatch job because I had an aviation degree. A degree in a related field can, to a certain extent, make up for a lack of experience. That said, I agree with Luigi. It may not be your lack of experience, but the way you are presenting yourself.
A few things to think on:
Have someone critique your resume. Ideally, it would be someone who works in Human Resources somewhere. It doesn't have to be an aviation company. Anyone working in an HR department ought to be able to give you some good tips. If you can't swing that, then find some dispatchers who have been successful at securing an entry level job (the job you are seeking) and ask to see their resumes.
Secondly, read a book on interviewing and interview questions. The more you understand the the rationale behind the questions, the better you will be able to prepare for the interview.
Finally, practice interviewing with a friend. Video record it, or do it on Skype or something similar. I did a Skype interview the other day, and I was surprised to observe several behaviors that I was not aware of.