Q: I didn't  get the storage I bought with my ipod

having an OS on a device and it's components on a device will take up a portion of the advertised space and in some cases the advertised size is slightly off the actual size.

if it's a new device contact apple for 90 days of free service

http://www.apple.com/contact/

Just what capacity iPod did you purchase?

What capacity do you think you have?

A 16 GB iPod will have about 12--13 GB available to the user. The differences is due to the OS taking up most of the difference. The remainder is due to how GB is advertised and how the OS reports it. See:

How OS X and iOS report storage capacity - Apple Support

Because of the latter, the larger the capacity the bigger the difference between advertised capacity and available capacity

How much was it off by? Marketers define storage sizes differently than engineers do, and computers usually report storage (RAM, disk, flash, etc.) the way engineers define it.

To an engineer, 1 KB = 1024 B = 2 to the 10th, 1 MB = 2 to the 20th, 1 GB = 2 to the 30th, 1 TB = 2 to the 40th, etc. These are more than the customary metric values of kilo-, mega-, giga-, etc. Marketers use the customary metric values, because they make it sound like it has more storage than it really does.

BTW, because RAM has to be balanced, even marketers use the binary meanings that engineers do.