The only way you can access apps is if they are on one of yuor home screens.
Please describe better how you say you can access it via the App store.
Does the FB app show as a purchased app in:
Sounds like you just can't find the FB app. Have you tried using the Spotlight search to find it?
If yo can find it you may have to connect the iPod to your computer and use iTunes to rearrange the apps so you can find it on a Home screen