Everyone has had failures. Everyone. The difference between people who ultimately become successful and people who ultimately fail is that the people who succeed don't let the failures stop them. They get back up and try again.
That being said, what did you learn from this experience? Did this class require that you do a lot of textbook reading? Did you have to write research papers? Did you have to read original source materials and then extrapolate? I'd bet that whatever it was, it was the first time you had to do that. You were learning on the job, so to speak. That doesn't always come easily or quickly. Take some time to figure out what you did well, and what you didn't do well, in terms of skills.
I'll tell you a few things I didn't know my freshman year of college. I went to a college that was extremely competitive, and my first year I struggled! Here's what I finally realized:
1) Don't take 4 hard classes at once. Chances are, some classes are going to be easier than others. You know from talking to others in your major what the easy classes are. Load your schedule with mostly easy classes and 1 hard class. This isn't high school, where you could handle 8 hard classes at once. College professors expect a lot more. Pace yourself.
2) Talk to upperclassmen and figure out what kind of study groups exist, or what kind of "underground" references you might have access to. For instance, I was in a sorority. In the library of my sorority house was a wall of file cabinets, organized by major and then class number. Whenever people got an A on a test, they would file it there. You could go there and read people's papers or tests to find out what the professor wanted, and what kinds of questions they would ask on the tests. If you can focus your studying in this way, you will be much more effective. You can't memorize a textbook, and there's no point in doing so. You need to figure out what the important things are, and study only those things. You'll learn more in less time.
Now, once you've put a plan together where you've determined:
1) Where you succeeded, and where you failed, in terms of your skills
2) What your schedule should be next time around (remember mostly easy classes, 1 hard class)
3) Where the resources are that can help you (more advanced students)
Once you have this figured out, go to your parents and tell them. Tell them that you have a D in this class, you will have to re-take it, you will pay the tuition if need be, and lay out what your plan is for improvement.
Like I said, everyone fails at something sometime. It's figuring out how you're going to succeed next time that will get you through this, and show your parents that you mean business. Take responsibility. Don't give up. The hardest things to do are the ones worth fighting for!