The recent COVID-19 crisis has shown that supply chain disruptions may lead to contagion in the financial system. The notion of financial systemic risk (SR) arises from the interconnectivity of financial institutions, e.g. on the interbank market. A shock to this system can originate from supply chain disruptions and for a coherent picture the notion of financial SR has to be extended by including firms and supply chains. Here we explore the relevance of supply chain contagion on financial SR. We use a unique dataset comprised of firm-level data of the Hungarian economy with time-resolved information on its supply chains as well as bank-firm credits as well as interbank loans. We identify and compare the relevance of the different channels through which financial institutions are exposed and show that taking the supply chain layer into account increases the expected losses of financial institutions from interbank exposure by a factor of 2. This highlights the need for a more integrated SR assessment by linking financial risks with the dynamics of the real economy.