Many autos are on the order of four feet tall, so a foot is a 25% increase in height. If the rack is close to the width of the vehicle, that means a 25% increase in frontal area, and - roughly - a 25% increase in aerodynamic drag at a given speed.
Additionally, most modern cars have fairly low "drag coefficients" - often as low as 0.2 or less, and "disrupting" the airflow can easily kick the Cd up to 0.4 or higher - which might mean a 100% increase in drag at the same frontal area. (1.25 x the area) x (2 x the Cd) gives you 2.5 times the drag at the same speed.
In the US, prevailing highway speeds are around 70 mph, and people consider "slowing down" to mean dropping to 65, or in the extreme to 60 mph. The drag is generally proportional to the square of the speed, so going 6/7 as fast reduces drag by (6/7)2 or to .73 x what you'd have "at speed." And 0.73 x 2.5 = 1.8 approximately.
If your engine is working 80% harder, I think I'd expect it to burn fuel a bit faster, and to burn more per mile.
Of course the typical auto carries a payload of about 200 lb (one passenger) so if it gets 30 mpg it's "payload efficiency" is 0.1 ton x 30 miles/gallon = 3 ton mile/gallon. Doubling the payload by putting 200 lb on the roof, even at the cost of increasing fuel consumption by 80%, improves the "payload efficiency" to 3.33 ton mile/gal.
Of course that semi that passed you while you were "slowed down" probably had a 30 ton payload (80,000 lb is a fairly common gross wt, with 60,000 to 65,000 lb in payload) and is typically getting >4 miles per gallon, so (s)he's moving 7 ton miles per gallon, or is more than twice as "efficient" as you are - comparing the trucker's worst case with your best of cases - without slowing down.(?)
There ain't no "free" way to move the freight. For small loads, it may be worth paying the fuel cost (and the nuisance penalties) for the convenience, but big trucks actually do do it better than you can for commercial-sized loads.