It is it, you can't play Apple Music on iPod Nano or iPod Shuffle, for Apple Music is a streaming music service, even you have subscribed Apple Music.
Here we talk about one method to convert Apple Music to iPod Nano or Shuffle audio format, and then you can transfer or sync them to iPod through iTunes.
First you need to free download Apple Music Converter (Mac Version and Windows Version) on your computer.
Second, Double click to install the Apple Music Converter, and run it. Here we take the Mac version for example.
Third, click the Add button, and then choose the downloaded Apple Music files to the filelist to convert.
And select the file you want to convert, click OK, and then all files you selected will be listed on the main window.
Moreover, click Setting button to set the output format and output path before the conversion as your need.
Finally, click the Convert button to start converting.
After the conversion, you can find the converted files through show in the Finder, and then use iTunes to sync the converted music files to your iPod Nano or Shuffle as you like.