How can I get a job when employers say I don't have enough experience?

I completed my bachelor’s degree in chemical and process engineering in July 2012. Since then, I have been struggling to find work with no luck. When I first applied for jobs, I was told that I had very little experience and I did not have a master’s degree. When I did not secure any interviews I worked voluntarily for a small company as a research and development engineer for a year and in the end they agreed to sponsor my postgraduate study.

I now have a year’s worth of experience in the energy and process industry and am studying for a master’s in chemical engineering. My sponsor liked my work, however, they have limited resources and so I have been applying for jobs elsewhere – but I am still being turned down. Either I get a reply stating that I do not have enough experience or my experience does not match any of their requirements even though I only apply when I see do meet the requirements.