Originally Posted by CanAutM3
The exact same thing hapenned to me a few years ago. It is the DCT oil pan that got damaged in my case. The DCT oil pan is made out of plastic, so it can easily get damaged. The DCT oil pan is not protected by the aluminum subframe under the engine. It is covered by one of those felted belly covers, so the oil leak was right under the engine.
In my case, there was barely any evidence of damage, the felted cover only had a very light scratch. It was the DCT plastic drain plug that got pushed in and stripped the thread in the pan.
If it is the case, the damage is not bad. You just need to replace the DCT oil pan. I don't know how much oil you lost, but I would not drive the car to avoid damaging anything further.
I believe the black thing I saw hanging out was the one in the middle of the plate under the engine