That's not entirely true. Gas engines are generally more efficient at higher throttle levels. The problem is if you're a "drive it like you stole it" kind of person that usually comes with speeding and a lot of gas-brake-gas-brake-etc... type driving. It's the brakes that are the problem, not the gas. You can accelerate briskly all you want, as long as you don't speed to the point where you have to slam on the brakes all the time.
I used to be a grandpa like driver, but I have noticed that slow acceleration doesn't really net me any improved gas mileage. Now I use as much gas as I feel like, and while I don't floor it I'm not easy on it either. The key is I get off it and coast once I hit the speed I'm looking for, which in town might be 35 - 40mph, or less. I used to annoy other drivers with how slow I accelerated, since abandoning that approach I have not noticed any decrease in mpg.