This article demonstrates how perceptual constraints of predators and the possibility that predators encounter prey both sequentially (one prey type at a time) and simultaneously (two or more prey types at a time) may influence the predator attack decisions, diet composition and functional response of a behavioural predator-prey system. Individuals of a predator species are assumed to forage optimally on two prey types and to have exact knowledge of prey population numbers (or densities) only in a neighbourhood of their actual spatial location. The system characteristics are inspected by means of a discrete-time, discrete-space, individual-based model of the one-predator-two-prey interaction. Model predictions are compared with ones that have been obtained by assuming only sequential encounters of predators with prey and/or omniscient predators aware of prey population densities in the whole environment. It is shown that the zero-one prey choice rule, optimal for sequential encounters and omniscient predators, shifts to abruptly changing partial preferences for both prey types in the case of omniscient predators faced with both types of prey encounters. The latter, in turn, become gradually changing partial preferences when predator omniscience is considered only local.