How dependent are European power systems and economies on natural gas? To answer this pressing question, we coupled a simulation model for assessing security of electricity supply and an economic optimization model. With this, we were able to analyze different reduction scenarios of the amount of gas utilized in the power sector. Our results show that reducing the amount of natural gas in the European power sector by up to 30% has a relatively moderate impact on the security of electricity supply. Restrictions of 40% or more result in substantially higher reductions in electricity demand shortfall and are associated with economic costs of more than EUR 77 billion. Furthermore, we demonstrate that a close coordination of gas distribution on a European level would be instrumental in mitigating negative economic consequences. Finally, it can be deduced that a coordinated delay of planned power plant shutdowns could effectively compensate for reduced gas volumes in the electricity sector.