- The backup that iTunes makes does not included synced media like apps and music. To be restored to the iPod during the restore from backup the synced media have to be in the iTunes library.
iTunes: About iOS backups
- You can redownload most iTunes purchases by:
Downloading past purchases from the App Store, iBookstore, and iTunes Store
However, only the current version of apps can be redownloaded.
Many developers when they updated their apps to support iOS 5 and 6 dropped compatibility for iOS 4.2.1 and earlier.
Your only way is if you have the version that was compatible on your computer such as in the recycle bin/trash or in a computer file backup. In that case delete the current version that is in your iTunes App library and replace it with the older version. Then sync.