Organic electrochemical transistors (OECTs) are receiving a great deal of attention as transducers of biological signals due to their high transconductance. A ubiquitous property of these devices is the non-monotonic dependence of transconductance on gate voltage. However, this behavior is not described by existing models. Using OECTs made of materials with different chemical and electrical properties, we show that this behavior arises from the influence of disorder on the electronic transport properties of the organic semiconductor and occurs even in the absence of contact resistance. These results imply that the non-monotonic transconductance is an intrinsic property of OECTs and cannot be eliminated by device design or contact engineering. Finally, we present a model based on the physics of electronic conduction in disordered materials. This model fits experimental transconductance curves and describes strategies for rational material design to improve OECT performance in sensing applications.