In this work, we continue to explore a method we have developed for modeling and correcting the effects of acoustic attenuation in optoacoustic tomography. We have shown previously that in the temporal frequency domain, the attenuated optoacoustic imaging equation is equivalent to an inhomogeneous Helmholtz equation with a complex wave number. We have also developed a numerical method for correcting for these attenuation effects simply by pre-processing of the one-dimensional time signal measured at each transducer location employed in the acquisition. We demonstrate through simulation studies that ignoring ultrasonic attenuation can lead to resolution degradation and distortion in reconstructed images because optoacoustic tomography relies on broadband detection and ultrasonic attenuation is frequency-dependent. We demonstrate that the proposed approach is able to compensate for the attenuation and improve the quality of the images. We also find that the effect of frequency-dependent attenuation remains significant even when narrow-band transducers, be they lowpass or bandpass, are used for detection.