Parameterization of zooplankton functional response is crucial for constructing plankton models. Theoretical studies predict enhancing of system stability in case the response is of sigmoid type. Experiments on feeding in laboratories tell us in favor of non-sigmoid types for most herbivorous zooplankton species. However, recent field observations show that the overall functional response of zooplankton in the whole euphotic zone can exhibit a sigmoid behavior even when the response for the same species in laboratory mesocosms is non-sigmoid. Here we propose a simple model explaining the observed alterations of functional response. We divide the euphotic zone into a number of layers and take into account the food-dependent migration of zooplankton. In each layer, the functional response (local response) is suggested to be non-sigmoid. We show that the overall response of zooplankton exhibits different behavior compared to the patterns of the local response. In particular, the model predicts emergence of a sigmoid type as a result of zooplankton accumulation and feeding in layers with high phytoplankton density. We show the importance of light attenuation by phytoplankton on the alteration of functional response. The modelling results allow us to hypothesize that the sigmoid functional response in real communities should emerge more often than it was suggested earlier based only on experimental studies on zooplankton feeding.