Creation of sustainable society and transition to low-carbon energy system are the main priorities of the EU policy. Energy poverty (EP) is one of the most important social problems linked to low-carbon transition as creation of carbon neutral societies requires to address other important sustainability issues linked with carbon-free future. Although assessment of EP is a prerequisite for designing policy initiatives to alleviate the problem. The article provides a methodological framework for the EP assessment taking into account goals of low-carbon energy transition and creation of sustainable carbon-neutral society. The proposed evaluation tool can be applied in different settings and used to track the relative progress of the countries in pursuing low-carbon transition and sustainable societies development. The Bellagio Sustainability Assessment and Measurement Principles (STAMP) were followed throughout the process of indicators selection and assessment. In order to determine countries’ achievements over time, the assessment was performed in 2010 and 2018 by applying two multi-criteria techniques. The results show that the Nordic countries stand out from other EU member states in terms of just low-carbon energy transition progress because of their low poverty indicators in households, high standard of living, and high share of renewable energy. •An innovative approach based on the Bellagio STAMP and multi-criteria techniques was developed.•Multi-criteria analysis and expert survey were applied for energy poverty measurement in the EU.•Sweden and Finland and other Nordic countries have received the highest ranking.•The lowest in the ranking was Bulgaria, following by Cyprus and Greece.