Herein, utilizing density functional theory (DFT) calculations, we have assessed the feasibility of single-atom-embedded C3N with various coordination environments of TM-C3, TM-C2N1, TM-C4, and TM-C2N2 for oxygen electrocatalysis. It has been proved that most TM-CxNy candidates are stable and all of them possess metallic features to ensure fast electron transfer. Importantly, Co-C2N2 is a bifunctional noble-free single-atom catalyst with low OER/ORR overpotentials (0.33/0.39 V). Furthermore, the impact of the coordination environment on the adsorption trend is revealed by the electronic properties of TM-CxNy. Considering that TM-d electron counts are multiplied by the sum of TM and C/N electronegativity, we propose a universal descriptor and offer more understanding of the coordination–activity correlation. Our findings not only show promising single-atom-embedded C3N candidates for oxygen electrocatalysis but also deeply unveil the impact of the coordination environment on catalytic activity.