Please help: Lacie 3TB connect to Airport Extreme for NAS?

Dear all, if someone can help me with this I'd be really grateful.

I want to connect a new Lacie 3TB external hard-drive to my AirPort Extreme to be able to use the Lacie as external network storage, but accessible via wifi.

My understanding is that it should just be a question of connecting the Lacie to the Airport Extreme, and then it should be available on the Finder as an external HD to which I could drag / pick files. I have formatted the Lacie connected to the Macbook Pro 15" (Mavrick) using the DiskUtility without problem.

However, when I connect it to the AirPort Extreme, it's not visible as a separate HD in my finder. Also when I go to DiskUtility, the Lacie doesn't appear in the list of disks (only the MBP SSD and Machintosh HD appears). When I however go to my Time Machine, then I can see that the Lacie appears in there.

The only think I can think of is that the Lacie somehow is seen as an extension of my AirPort so that the Lacie storage is available for the Time Machine, instead of being seen and usable as a separate HD for storage on the wifi?

When I connect the Lacie to the MacBook then it appears under Devices and I can of course drag'n drop. I would however like that it works like that, but over the wifi system so that it's available when I'm home on my wifi network, without having to plug it in (yes, I know transfer rates will be affected, but that's an inconvenience I'm willing to live with for the benefit of having it on the wifi system so I don't need to fiddle with cables).

VERY grateful if someone can help me resolve this problem!

R