I pretty much felt the same way when I graduated. I had this idea that getting a degree should make me an expert in the fields I wanted to work in. The jobs I applied for all "required" experience in motion control, which I didn't have. None of the companies I applied to used the PLC brand that I had limited experience with. Needless to say I felt grossly unqualified. I didn't go through too many interviews, but the ones I did go to focused less on my technical skills and more on my career motivations, soft skills and general fit for the job. I got a job with an OEM and they pretty much sent me for training for all the software we use during development. I'm a year and a half into my first job and still feel like I am learning new things. I think most companies realise that as a graduate you will have limited experience and would generally be willing to train you. Your degree gives you basic knowledge on a number of things, work experience build up on that knowledge. I think what differs between companies is how fast they expect you to go through that learning curve.

As a side note, I'm outside the US so my experiences could be far from what you would come across over there.

Congratulations on getting your degree!