Brand new iPod touch 4th generation VERY short battery life.

So the other day I went in to replace my old iPod touch for a new one because the home button was getting stuck and wouldn't work. So everything worked fine and I got the new ipod. Well It's been a few days and I've noticed that the battery life on this ipod isn't long at all. It'll last me maybe 30 minutes of usage. I've done everything I can to try and save battery life and it kind of helps, but not really. When I got this new iPod, I restored it from a previous backup instead of setting it up as a new iPod. I've read that doing this is the number one reason for battery loss in new iPhones and iPods. Is this true??

What should I do? I'm guessing that the battery isn't bad because it's BRAND NEW! I was going to take it to Apple, but I'm not sure if they'd find anything wrong with it since it is a brand new battery. PLEASE HELP!