No iTunes content is included with the iPhone's backup.
You should have included your iTunes media folder with your computer's backup per the instructions included with this link.
iTunes includes an option to transfer iTunes content that was purchased/downloaded from the iTunes store from an iPod, iPad, and iPhone, but this is for iTunes content that was purchased/downloaded from the iTunes store only.
First you need to re-authorize your computer with your iTunes account with iTunres if you haven't already done so.
With your iPhone connected and without syncing, at the iTunes menu bar go to File and select Transfer Purchases From - the name of your iPhone.