Ultra-reliable and low-latency communication (URLLC) is one of the key applications in fifth generation (5G) cellular networks, which requires extremely high reliability (\sim99.9999) 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.