Protected areas aim to conserve nature, ecosystem services, and cultural values; however, they have variable success in doing so under high development pressure. Southeast Asian protected areas faced the highest level of human pressure at the turn of the twenty-first century. To estimate their effectiveness in conserving forest cover and forest carbon stocks for 2000-2018, we used statistical matching methods to control for the non-random location of protected areas, to compare protection against a matched counterfactual. We found Southeast Asian protected areas had three times less forest cover loss than similar landscapes without protection. Protected areas that had completed management reporting using the Management Effectiveness Tracking Tool (METT) conserved significantly more forest cover and forest carbon stocks than those that had not. Management scores were positively associated with the level of carbon emissions avoided, but not the level of forest cover loss avoided. Our study is the first to find that METT scores could predict the level of carbon emissions avoided in protected areas. Given that only 11% of protected areas in Southeast Asia had completed METT surveys, our results illustrate the need to scale-up protected area management effectiveness reporting programs to improve their effectiveness for conserving forests, and for storing and sequestering carbon.