Moving apps to SD (which only ever moved part of the app) isn't supported in that version of Android (unless the manufacturer has hacked the feature back in). So if when you look at a downloaded app in Settings > Apps > Downloaded and there isn't a "move to sd" button, there's no way of doing it without rooting the device.
You cannot move pre-installed apps anyway, but equally they live in a different partition so aren't using "your" space. App data do however use space, so if your pre-installed apps are using a lot of data storage that could be a problem. Best to check that: Settings > Apps > All, sort by size, then look at big ones and see how much data they are using. Beware that in android 4.1 "internal" SD card and your internal storage are the same thing, so if an app has a lot of stuff stored in a folder there that may be contributing to the problem.