Most animals are faced with the challenge of securing food under the risk of predation. This frequently generates a trade-off whereby animals respond to predator cues with reduced movement to avoid predation at the direct cost of reduced foraging success. However, predators may also cause prey to be apprehensive in their foraging activities, which would generate an indirect ‘apprehension cost’. Apprehension arises when a forager redirects attention from foraging tasks to predator detection and incurs a cost from such multi-tasking, because the forager ends up making more mistakes in its foraging tasks as a result. Here, we test this apprehension cost hypothesis and show that damselflies miss a greater proportion of their prey during foraging bouts in response to both olfactory cues produced by conspecifics that have only viewed a fish predator and olfactory cues produced directly by fish. This reduced feeding efficiency is in addition to the stereotypical anti-predator response of reduced activity, which we also observed. These results show that costs associated with anti-predator responses not only arise through behavioural alterations that reduce the risk of predation, but also from the indirect costs of apprehension and multi-tasking that can reduce feeding efficiency under the threat of predation.