We present a decentralized feedback-aided Irregular Repetition Slotted ALOHA (IRSA) scheme that improves energy efficiency. The scheme divides the IRSA MAC frame into several sub-frames, performs tentative decoding after each sub-frame, and uses limited feedback for users to detect whether their packet has been decoded at the receiver. Once a user detects that its packet is decoded, it stops transmitting its remaining replicas, resulting in a decrease in the expected number of transmitted packet replicas and an increase in energy efficiency. For analysis, we employ a graph-based representation of the successive interference cancellation decoding of IRSA. We prove several results for a fixed graph, and extend our analysis to a randomly selected graph to derive the efficiency of the proposed scheme. Numerical results show that the proposed feedback-aided IRSA solution outperforms standard IRSA and performs similarly to the best known Coded Slotted ALOHA (CSA) schemes. Also, the proposed scheme achieves efficiencies significantly larger than the threshold of 0.5 which is an upper bound for standard IRSA.