The space-air-ground integrated network (SAGIN) is a critical part of the 6G network and has recently attracted researchers' attention. Compared to traditional ground network, SAGIN has a wide coverage area and enables seamless Internet access for users worldwide. However, due to its structural complexity, diverse services, and the heterogeneous nature of its resources–including bandwidth, CPU, and storage–the orchestration of these multidimensional resources in SAGIN poses a significant challenge. Through network virtualization technology, the resource orchestration of SAGIN can be transformed into a virtual network embedding (VNE) problem. To address the issue of high energy consumption, this paper introduces an innovative energy-aware VNE algorithm that integrates deep reinforcement learning (DRL) with graph convolutional network (GCN). In particular, during the node mapping phase, we develop a GCN-based policy network that effectively extracts network features by aggregating information from adjacent nodes through GCN. Furthermore, Chebyshev polynomials are employed to approximate the graph convolution kernel, which significantly reduces the algorithm's computational complexity. To minimize energy consumption during the link mapping process, we have proposed an energy-first K-shortest path algorithm. Finally, we simulated the proposed algorithm, GD-EA-VNE, to evaluate and verify its effectiveness.