Climate adaptation actions can be energy-intensive, but how adaptation feeds back into the energy system and the environment is absent in nearly all up-to-date energy scenarios. Here we quantify the impacts of adaptation actions entailing direct changes in final energy use on energy investments and costs, greenhouse gas emissions, and air pollution. We find that energy needs for adaptation increase considerably over time and with warming. The resulting addition in capacity for power generation leads to higher greenhouse gas emissions, local air pollutants, and energy system costs. In the short to medium term, much of the added capacity for power generation is fossil-fuel based. We show that mitigation pathways accounting for the adaptation-energy feedback would require a higher global carbon price, between 5% and 30% higher. Because of the benefits in terms of reduced adaptation needs, energy system costs in ambitious mitigation scenarios would be lower than previous estimates, and they would turn negative in well-below-2-degree scenarios, pointing at net gains in terms of power system costs.