In this study, we adopt a model-based correction method to reduce the finite aperture effect in photoacoustic tomography (PAT)--the tangential resolution deteriorates as the imaging point moves away from the circular scanning center. Such degradation in resolution originates from the spatial impulse responses (SIRs) of the used finite-sized unfocused transducer. Based on a linear, discrete PAT imaging model, the proposed method employs a spatiotemporal optimal filter designed in minimum mean square error sense to compensate the SIRs associated with an unfocused transducer at every imaging point; thus retrospective restoration of the tangential resolution can be achieved. Simulation and experimental results demonstrate that this method can substantially improve the degraded tangential resolution for PAT with finite-sized unfocused transducers while retaining the radial resolution.