Applying for experienced jobs as a fresher

I encounter a lot of job openings which require some experience, say 1 year or 2 years. Even though I feel I would be a great fit being a fresher and someone with little experience (goggle summer of code and only intern experiences), I end up not applying as it would need a referral and I would possibly be wasting time of the person who would be giving me referral as possibly my application might not even get considered (as I fail the experience benchmark). Can anyone suggest what should I do? Is there a strong cap about the experience required ?