Unmanned aerial vehicles (UAVs)-enabled base stations (BSs) can boost the system performance of the terrestrial networks with device-to-device (D2D) communication in the scenarios that fixed BSs in the ground are not available. However, the serious interference among UAVs and multiple D2D pairs is more challenging than the terrestrial case because UAVs are changing the networks topology frequently over time. In this paper, the power control optimization is investigated for D2D communications underlaying UAV-assisted access systems, where a UAV-enabled BS serves multiple users, and the remaining users communicate with each other with the assistance of the UAV, also referred to as D2D pairs. With the aim of throughput maximization, we need to address a non-convex optimization. To this end, difference of two convex functions (D.C.) programming is invoked to solve the formulated optimization, which can obtain suboptimal solutions. Considering the UAV's limited energy and low computational capability, we further design a low-complexity power control algorithm by exploiting the Hessian matrix's structure. Simulation results show that the proposed algorithms perform quite well for all considered scenarios. Both of them can improve the system throughput dramatically. Moreover, the low-complexity algorithm produces almost the same throughput as the D.C. programming method with much lower computation burden.