Is it a Windows computer or a Mac?
Also, do you have an iCloud account and have it setup on the iPhone (even if you are NOT using it to backup the iPhone)?
If you have iCloud setup on the iPhone and have it setup to sync contacts, then the contacts will be synced by iTunes and by default will NOT sync through iTunes even through you are backing up the iPhone through iTunes. If that is the case, you can go to the iCloud site (www.icloud.com) and log into your account and get access to your contacts.
If you do not have iCloud setup, then iTunes MIGHT be syncing your contacts depending on whether that option is checked. Assuming it is checked, then if it is a Mac, then they will sync with the Address Book application built into the Mac OS. If is a Windows computer, then I believe it only sync with Outlook if it is installed...I am not sure what happens otherwise.
I believe if iTunes is not syncing the contact, then I believe it might backup the contacts with everything else....but if so, there is not way to specifically get to it other than to restore the backup by way of iTunes...at least that I know of.