The find my iDevice works through iCloud. What you needed to have done before it went missing was setup an iCloud account on the device, then enable the find my device slider setting to "ON" under that account's settings.
If you did not do that, it is not trackable.
There is no way to track it by serial number.
Also, in order to be trackable it has to be powered on and connected to a data connection. A wifi-only device like an iPod Touch powers off the wifi radio when running on the battery, so if it has gone into sleep mode, it would not be trackable until or unless woken up by someone so it could re-acquire a data connection with a wifi network.
The SN is useless in trying to locate your Touch. Find My Phone doesn't work that way. The only way to locate any lost/stolen iPhone is through Find My Phone or a similar app. However, this requires that Find My Phone be setup/activated, on your phone, before it was lost/stolen. You would then login at iCloud.com & try to locate it. This requires the phone be turned on & have an Internet connection. There is no other way to locate a lost/stolen iPhone.