Photoacoustic tomography (PAT), also known as thermoacoustic or optoacoustic tomography, is a hybrid imaging modality that reconstructs the electromagnetic absorption properties of biological tissue from knowledge of acoustic signals produced by the thermoacoustic effect. Because the propagation of acoustic signals is most generally described by the 3D wave equation, PAT is an inherently 3D imaging modality. Due to the the limited penetration depth of the probing electromagnetic fields and the limited availability of 3D ultrasound detector arrays, a simplified two-dimensional (2D) PAT measurement geometry is used in many current experimental implementations. However, in this case, when unfocused transducers are employed, the acquired data are not sufficient to invert the 3D imaging model and ad hoc reconstruction procedures are employed. In this work we numerically investigate 2D and 3D PAT assuming an ultrasound transducer having an anisotropic detection response. The uncompensated effects of an anisotropic detection response on images reconstructed using a point-detector assumption are demonstrated.