Ugh... my "Backup" didn't include Music??? (iPod replaced)

So, I go to the Apple Store and they determine we need a replacement of our iPod 5th gen, but I hadn't made a backup, so they say go home and make a Backup and then you'll be able to restore everything.

Did that, switched devices, and now, after restoring, NO music. Photos are fine.

Sigh... why doesn't the Apple Store OR the Genius Bar reservation signup website say AND SYNC?

Is there ANY way I can recover my Music Library (songs, albums, playlists) that was saved on my previous iPod??

Most of it was imported from mp3s I own and was added by dropping mp3s from Finder onto the "On This iPod" window in iTunes, which I believe bypassed putting it into the Library? Not sure how that works, but still figured a "backup" would actually backup the stuff ON the iPod. sigh

I didn't realize that a Sync was also necessary... figured it would happen automatically when I backed up. (or am I misunderstanding what other threads have stated?)

iTunes makes me crazy sometimes...

and it seems like syncing my entire "library" would put a bunch of stuff that I have on my other iDevices, which I don't want at all.

any help is appreciated.