In this paper, we consider an Internet of Things (IoT) network supporting latency-critical transmissions to multiple nodes in the finite blocklength regime. An energy efficiency maximizing design is provided via efficiently jointly allocating the power and blocklength among the transmissions to different nodes, while guaranteeing per-node constraint of reliability. To address the formulated non-convex problem, we propose a Majorization-Minimization-based approach. Specifically, we tightly approximate the problem at each local point by introducing an auxiliary constant. Then, we rigorously prove the convexity of the conducted local problem. By successively optimally solving each convex local problem, a near-optimal solution is finally achieved. Via simulations, we demonstrate the performance advantages of the proposed joint design.