It's a vicious circle, can't get a job without experience, can't get experience without a job.
After graduation it took me 11 months and over 200 applications. Initially I took a part-time community service type job in a research charity (explaining biochemistry research papers to non biochemists). The next interview I had they were going through my CV and, as expected, commented on my lack of employment. I was able to explain this had changed and talked about the part-time work I was doing and they hired me.
I Know it's difficult but persevere. The alternative is to do post-graduate qualifications and enhance your prospects that way.