According the the tech specs page for the current iPod nano
http://www.apple.com/ipod-nano/specs/
The system requirements (for the computer syncing iPod) says
Mac: OS X v10.7.5 or later, and iTunes 12.2 or later
PC: Windows 7 or later, and iTunes 12.2 or later
That means your computer (Mac or Windows PC) needs to run at least OS X 10.7.5 (Lion) or Windows 7, to run a supported version of iTunes. If the latest version of iTunes you can currently run in 11.4, you'll need to upgrade your computer's OS (if possible).
For a Mac, the latest version of OS X is El Capitan (10.11). This Apple web page has information about upgrading
http://www.apple.com/osx/how-to-upgrade/
If your Mac is too old to support El Capitan, it may still allow at least OS X 10.7.5.