In vivo attenuation slope measurements usually utilize the backscattered signal from pulse/echo ultrasound. In this work the down shift of the center frequency of an emitted ultrasound pulse with penetration depth is utilized to estimate the attenuation slope. A diffraction correction of the focused ultrasound source is performed by measuring the reflection from a planar surface positioned throughout the depth of focus. A focused single element transducer with a measured center frequency of 8.2 MHz and a fractional band width of 72% was used to interrogate four tissue mimicking phantoms. The scatterers in the tissue mimicking phantoms were glass spheres embedded in a gelatin/milk matrix. In one set of the phantoms, the backscattering strength was varied; in the other set of phantoms the attenuation slope was varied. The attenuation slope (ASBS) was estimated using pulse/echo data obtained by scanning the phantoms. The "true" attenuation slope (ASThru) was obtained from two independent insertion loss measurements performed at two different laboratories. The relative error of ASBS was investigated for different regions of interest (ROI) for all phantoms. Three different axial and lateral ROI sizes were tested. It was observed that the average relative error (average over all four phantoms) changed by less than three percent when the lateral size of the ROI was decreased by seventy percent. The axial size of the ROI was changed by thirty percent whereas the average error changed by less then three percent.