I have a 1st gen iPod shuffle, and it works fine with iTunes 12. (The clip-on 2nd gen shuffle also works.) It is recognized properly and shows up on the "device button," by itself and with other devices connected at the same time. OS X 10.10 on a Mac mini with USB 2.0 ports.
The most common failure point on the 1st gen shuffle is the built-in USB plug. It tends to wear out from repeated connects and disconnects. Often, it will still connect for power (to charge the battery), but not for data. However, if it is recognized using Windows Explorer, that is not the problem.
When you connect the shuffle, what does shuffle's light do? Is it blinking or solid (or not on)?
Also, if you are using iTunes 12 for the first time, the iPod "appear" on the iTunes window as a "device button." It is on the horizontal bar that goes across the iTunes window, near the top. The button's tiny icon looks like the device. Also, if you use the Playlists view, the sidebar appears along left side of iTunes window, and the iPod is show in the sidebar, under Devices.