Increasing the coverage of effectively managed protected areas (PAs) is a key focus of the 2020 Aichi biodiversity targets. PA management has received considerable attention, often based on the widely-held, but rarely examined, assumption that positive conservation outcomes will result from increased PA management inputs. To shed light on this assumption, we integrated data on PA management factors with 2006-2011 avoided forest degradation and deforestation across the Peruvian Amazon, using a counterfactual approach, combined with interviews and ranking exercises. We show that while increasing PA management input to Amazonian PAs tended to reduce likelihoods of forest degradation and deforestation, the associations were weak. Key challenges facing PAs ranked by PA managers included wider law enforcement, corruption and land title issues, rather than local management factors. We therefore encourage the post-2020 conservation targets to adopt holistic approaches beyond PA management, incorporating political, institutional and governance contexts across scales.