I've hired a lot of people, and had to apply for a few jobs in my time as well.
Don't downgrade your qualifications, address that concern up front with the interviewer. Back in the Tech Wreck of 2001 I got a "don't come Monday", and after spending a month applying for every job, I walked into the local hardware, filled in the application and got the interview. The manager asked me the same question, and I answered honestly that I didn't plan to be there for the rest of my life but I would give them the benefit of all my experience whilst I was there. I worked there for about three months, became a manager and got promoted to the Head Office group.
In my current role we have a crap position of project dogs body. We used to hire older ladies with no career aspirations, thinking they would put up with it, but this was never satisfactory (our fault, not theirs). Instead we decided to get hotshot grads straight out of uni, knowing they weren't going to stick around but also knowing they would learn fast an excel whilst with us. Never once regretted that approach.
Even now I have a bunch of Gen Ys who work for me and everyone of them is a star in the making, as good a worker as one could meet.
Good luck in your search, don't sweat the jobs you missed out on, just keep looking for the manager/employer who values experience.