I hauled 2 bikes on a hitch rack with my Honda Civic. We were going a few hundred miles with a headwind on 70 mph interstates mostly. I did check the mpg; I would have done better with my Chevy Silverado pickup I replaced the Honda with. I couldn't hardly get the car to go 70...kept on trying to downshift to get up to speed.
Are you really describing a hitch rack, not a roof rack? If so, that must have been a very old, very high mileage and very worn out Civic.
I've driven thousands and thousands of miles with one or two bikes on rear hitch racks and the effect on fuel mileage has been minor and the cars had no problems maintaining speed. Hitch racks have far less aerodynamic drag than roof racks.