DNA metabarcoding of faeces or gut contents has greatly increased our ability to construct networks of predators and prey (food webs) by reducing the need to observe predation events directly. The possibility of both false positives and false negatives in DNA sequences, however, means that constructing food networks using DNA requires researchers to make many choices as to which DNA sequences indicate true prey for a particular predator. To date, DNA-based food networks are usually constructed by including any DNA sequence with more than a threshold number of reads. The logic used to select this threshold is often not explained, leading to somewhat arbitrary-seeming networks. As an alternative strategy, we demonstrate how to construct food networks using a simple Bayesian model to suggest which sequences correspond to true prey. The networks obtained using a well-chosen fixed cutoff and our Bayesian approach are very similar, especially when links are resolved to prey families rather than species. We therefore recommend that researchers reconstruct diet data using a Bayesian approach with well-specified assumptions rather than continuing with arbitrary fixed cutoffs. Explicitly stating assumptions within a Bayesian framework will lead to better-informed comparisons between networks constructed by different groups and facilitate drawing together individual case studies into more coherent ecological theory. Note that our approach can easily be extended to other types of ecological networks constructed by DNA metabarcoding of pollen loads, identification of parasite DNA in faeces, etc.