In this paper, we consider a downlink multiuser network operating with finite blocklength codes under statistical quality of service (QoS) constraints. An optimal power allocation algorithm is studied to maximize the normalized sum throughput under QoS constraints. We first determine the finite blocklength (FBL) throughput formulations and subsequently state optimization problems. We show the convexity of the power allocation problem under certain conditions and propose an optimal algorithm to solve the problem. Via numerical analysis, we demonstrate the performance improvements with the optimal power allocation. In addition, we provide interesting insights on the system behavior by characterizing the impact of the error probability, the QoS-exponent and blocklength on the performance.