This is just a guess, but I think some kind of soap would cut the hydrocarbons in the gasoline, and get them to come loose from the surfaces they are on. Do the rug while outside the vehicle and elevated like on saw horses. The hotter the water the better.
Mix up a few gallons of hot water with some good sink type dish soap like Palmolive, and some Johnsons Baby Shampoo. Scrub and sponge the area, and rinse well. A hot water rinse would work better than cold water. You can put a garden hose on the bottom of a hot water heater to get hot water if you do not have any other way to get hot water to a hose. If you use the bottom of a water heater for your hot water, be sure to run several gallons first to get rid of the sediment that will be in the water at the bottom of the water heater, before you use that water for cleaning. You might have to give the water heater time to heat the replacement water after you do the run of water to get rid of sediment.
Do a second wash and rinse with hot water and Johnsons Baby Shampoo without the Palmolive if the first wash leave any smell.
If you do end up with a sligh smell of baby shampoo for a few days it is not as bad as gasoline.