As energy demands continue to rise, energy production from sources including natural gas is expected to rapidly accelerate in the coming decades, potentially leading to substantial land-use changes. In the Appalachian region of the United States, natural gas development often occurs in forested areas, which can cause high levels of forest disturbance and loss. Here, we use nationwide forest inventory and remotely sensed data in a Bayesian model to quantify the impacts of natural gas development at fine spatial resolutions between 2008-2021. Based on well permit locations in the states of Ohio, Pennsylvania, and West Virginia, the analysis quantifies disturbance area, forest carbon loss, and opportunity cost with associated levels of uncertainty at the pixel-level. Overall, we estimate 10,854 ha of forest land were disturbed, resulting in 542,675 Mg ($\pm$ 4,275) of forest carbon loss. The opportunity cost associated with these disturbances is estimated to be 575,246 Mg ($\pm$ 30,774). Pixel-level estimates are generated for individual well sites, which can be aggregated to the county-level to highlight regional patterns. Specifically, we observe greater levels of disturbance in Northern West Virginia, while opportunity costs are greatest for large forested counties in Northeastern Pennsylvania. This study demonstrates the importance of quantifying balances and tradeoffs between energy production and forest ecosystem services, and provides important insights into the impacts of energy development on forest carbon.