In response to the security threats in wireless networks with concurrent device connections, deploying Intrusion Detection Systems (IDS) at the network edge is a promising strategy. However, this approach must take into account the resource constraints incurred by power-limited edge devices, requiring a lightweight solution to IDS. At the same time, the lightweight IDS solution has to minimize performance degradation as higher detection performance is also a key requirement of IDS. In this paper, we design a lightweight autoencoder with explainability, employing the Shapley value to measure unit importance and link importance. This approach can selectively activate only critical components, thereby reducing the complexity for IDS while effectively lowering its performance degradation. We confirm that the proposed algorithm is robust against the harsh sparsity of the autoencoder. Moreover, the sparsity of the proposed lightweight autoencoder can be easily manageable, such that it can be controlled to satisfy the potential constraints of power-limited edge devices. Therefore, the solution is a suitable algorithm for IDS that can be deployed on edge devices in wireless networks.