Summary: We prove an energy inequality for nonlocal diffusion operators of the following type, and some of its generalisations: \[ L u(x) := \int_{\mathbb{R}^N} K(x,y)(u(y)-u(x))dy, \] where \(L\) acts on a real function \(u\) defined on \(\mathbb{R}^N\), and we assume that \(K(x,y)\) is uniformly strictly positive in a neighbourhood of \(x=y\). The inequality is a nonlocal analogue of the Nash inequality, and plays a similar role in the study of the asymptotic decay of solutions to the nonlocal diffusion equation \(\partial_t u = Lu\) as the Nash inequality does for the heat equation. The inequality allows us to give a precise decay rate of the \(L^p\) norms of \(u\) and its derivatives. As compared to existing decay results in the literature, our proof is perhaps simpler and gives new results in some cases.