Don't let job hunting get you down.
I have a BA and an MSc, which puts me into the top 1% of the world in terms of education. I went to good universities and got good grades from a good school, I had part-time jobs and I even did some volunteer work. My CV looked good, and it presented me as a well-rounded person with varied interests and a wide range of skills (and maybe some b/s too, but who's keeping track?)
When I completed my Masters Degree, I couldn't find a "real" job for love nor money. Fortunately, I'd been working part-time in a pub kitchen during my course and I was able to get more hours there to keep the money coming in whilst I looked for work, but all my education and extra-curricular activities meant nothing when I never got past the first hurdle. The truth was simple; the job market was hell. There were hundreds of people applying for every job, and, for all of my fancy education and volunteer work, there was another person with a decade or more of relevant workplace experience. I simply could not compete.
It took nine months for me to find a "real" job (that's no disrespect to anyone working in a pub, I loved that job, but it was never going to be my career, and my parents gave me hell for even considering it) and even then, the job I found was utter garbage. I was paid as much as I was earning working in the pub, but I was now sat behind a desk and wearing a shirt and tie each day. It was a step up, but it was a miserable job and it made me miserable. I felt like I put my entire life on hold for the years that I worked there, building up enough "experience" to move on to a good job. Now, though, I have that job, and it's great. I've got a good job at a progressive company, I've bought a really nice car in the past six months and I'm now saving up so that I can put a deposit down on a house next year.
I got rejected more times than I could keep track of. I would apply for fifty to a hundred jobs each day, and I wasn't just applying for any old job, I was applying for jobs that said "no experience needed", and for jobs where my degrees were relevant. It's not great, and you do feel like you're doing the best you can and getting nowhere, but you have to keep plugging at it. I got a job, and it was lousy, so I kept going, and now I finally feel like my life is moving in the right direction. Just keep at it, because as long as you're trying, you're not failing.
And one final piece of advice that I learned; there's a big gulf between "failing" and "not succeeding". The world isn't so black and white, and you shouldn't be beating yourself up about it.