Gutman defined the energy \( \mathcal E(G) \) of a simple graph \( G \) with vertex set \( V=\{v_1,v_2,\ldots,v_n\} \) as the sum of the absolute values of eigenvalues of the adjacency matrix of \( G \), which has been studied extensively in mathematical chemistry. Espinal and Rada (Graph energy change due to vertex deletion, MATCH Commun. Math. Comput. Chem. 92(2024), 89-103) proved that \[ (n-2)\mathcal E(G)\leq \sum\limits_{i=1}^n\mathcal E(G-v_i). \] In this paper, we generalize the above result by Espinal and Rada and prove that for any positive integer \( k\leq n-2\), then \[ \dbinom{n-2}{k}\mathcal E(G)\leq \sum\limits_{W\in \mathcal G_k}\mathcal E(G-W), \] where \( \mathcal G_k=\{W\subset V||W|=k\} \) and \( G-W \) is the subgraph of \( G \) by deleting all vertices in \( W \) from \( G \). Particularly, we show that if \( n\geq 3 \), then \[ \mathcal E(G)\leq \frac{2}{n-2}(2a+\sqrt{2}b+c), \] where \( a,b \) and \( c \) are the numbers of triangles in \( G \), induced subgraphs of \( G \) isomorphic to \( P_3 \) and \( K_2\cup K_1 \), respectively.