Sound radiation of most natural sources, like human speakers or musical instruments, typically exhibits a spatial directivity pattern. This directivity contributes to the perception of sound sources in rooms, affecting the spatial energy distribution of early reflections and late diffuse reverberation. Thus, for convincing sound field reproduction and acoustics simulation, source directivity has to be considered. Whereas perceptual effects of directivity, such as source-orientation-dependent coloration, appear relevant for the direct sound and individual early reflections, it is unclear how spectral and spatial cues interact for later reflections. Better knowledge of the perceptual relevance of source orientation cues might help to simplify the acoustics simulation. Here, it is assessed as to what extent directivity of a human speaker should be simulated for early reflections and diffuse reverberation. The computationally efficient hybrid approach to simulate and auralize binaural room impulse responses [Wendt et al., J. Audio Eng. Soc. 62, 11 (2014)] was extended to simulate source directivity. Two psychoacoustic experiments assessed the listeners' ability to distinguish between different virtual source orientations when the frequency-dependent spatial directivity pattern of the source was approximated by a direction-independent average filter for different higher reflection orders. The results indicate that it is sufficient to simulate effects of source directivity in the first-order reflections.