Yikes!! That was some puddle. Still, the cover should not have come loose if it was properly installed. Looks like some custom parts there that are white (torsion bar?), so that could explain it. Obviously, you can't drive it like that. But if you take off the loose shield, you can drive it. I would not leave it that way, though. I'd want to get it covered back up to get the airflow back to where it should be and protect anything that the shield might be protecting.
Dealer told me that was the plastic cover for the gas tank along with other connections. Had it removed since I tried to remove it myself yesterday but was not able to. EDIT: Is it safe to drive, for a longer period of time (months), without that plastic cover? Concerned because ground clearance is low. The white thing is TRD rear sway bar. Good thing I did not proceed to get the lowering springs EDIT 2: This is the video of that incident that took out that plastic cover. Probably, the civic dropped "something" after driving through that puddle and that thing took mine out.