If you spend longer to accelerate more gradually in thick air, then you potentially use more fuel to get to the same speed.
Acceleration is proportional to thrust, but energy expended is the time integral of thrust and velocity, so depends on the speed profile as drag builds on takeoff, and then needs to be tweaked for the relationship between thrust and fuel consumption.
Just along the runway, it seems reasonable that reaching the same take off speed more slowly will consume more fuel, as while the aircraft has the same energy when it leaves the ground, when derated there's a longer track of moving air stirred up behind you.
However, is the motivation for derating is about saving money by protecting the engine from unnecessarily high temperatures? In that case, a few kg of fuel is cheaper than an overhaul.