Natural and anthropogenic disasters frequently affect both the supply and demand side of an economy. A striking recent example is the COVID-19 pandemic which has created severe industry-specific disruptions to economic output in most countries. Since firms are embedded in production networks, these direct shocks to supply and demand will propagate downstream and upstream. We show that existing input-output models which allow for binding demand and supply constraints yield infeasible solutions when applied to pandemic shocks of three major European countries (Germany, Italy, Spain). We then introduce a mathematical optimization procedure which is able to determine best-case feasible market allocations, giving a lower bound on total shock propagation. We find that even in this best-case scenario network effects substantially amplify the initial shocks. To obtain more realistic model predictions, we study the propagation of shocks bottom-up by imposing different rationing rules on firms if they are not able to satisfy incoming demand. Our results show that overall economic impacts depend strongly on the emergence of input bottlenecks, making the rationing assumption a key variable in predicting adverse economic impacts. We further establish that the magnitude of initial shocks and network density heavily influence model predictions.