At the altitude they used to fly at there wasn't much air resistance. I think it's more the acceleration and climb out phases when they are using the reheat (aka afterburner). Cruising at ~50-60000 feet, Concorde was pretty efficient, comparable fuel burn to a 747 from that era, but the engines were super inefficient in all the other phases of flight. I've heard it said that it used more fuel to taxi to the end of the runway at Heathrow than a modern A320 would use to fly London to Paris. (Someone else can google that to see if it's true! I can't be bothered.)