Ultra-reliable and low-latency communication (URLLC) is one of the key applications in fifth generation (5G) cellular networks, which requires extremely high reliability (similar to 99.9999%) and low latency (< 1 ms). In this paper, the energy efficiency (EE) of multi-user multicarrier amplify-and-forward (AF) networks is maximized under short packet transmission. Accordingly, we formulate an energy-efficient resource allocation problem to jointly optimize the transmit power, subcarrier pairing and allocation, and error probability with finite block-length codes subject to the constraints of the decoding error probability of each user pair, subcarrier pairing and allocation and total transmission power. The formulated problem is non-convex and hence difficult to solve. We analyze the structure of the problem and hence convert it into a convex problem which is approximately equivalent to the original one. An efficient algorithm is also proposed which is capable of producing a near-optimal solution. Simulation results validate the effectiveness of the proposed algorithm that supports energy-efficient URLLC, by showing the impact of various system parameters on EE.