That is not right. I just had a phone that had that same issue. A Huawei mercury. On the days that would happen, my battery would drain 2 or 3 times faster than normal if not more. No matter what I was, or was not doing with the phone. I had too keep auto sync, background data, maps, and play store off at ALL times to slow this down. It was bs. I've never had or seen another phone do this. You should either never see Android System in the battery use screen, or at least never anywhere near the top.
I switched phones, and once again I'm back to normal. I have an HTC One v, and just like I'm use to the Android system never gets above like 3 to 5 percent. I have my background data on, my auto sync on for all my app including email, and I'm just fine now battery lasts all day easily. If you have just gotten this phone recently I would attempt to either exchange it and see how the other 1 works for get your money back and try a different phone. That is definitely not right.