Perceptual quality for media compression algorithms is traditionally evaluated through user studies. Such studies are time consuming, laborious and expensive, slowing down the development of new signal processing algorithms. To address this problem, a number of algorithmic quality prediction methodologies have been developed in the audio and video fields, something that is currently lacking in haptics research. In this paper, we present a novel method for predicting the perceptual quality degradation of compressed haptic texture signals. For this purpose, abstract perceptual features like Roughness, Brightness, etc. that capture the subjective experience of textures are exploited, in addition to low-level psychophysical models from the literature. As compared to the state-of-the-art, the presented prediction methodology shows an approximately 30% improvement in explaining the variance in the perceptual data.