An efficient Perceptually Attentive (PA) Super-Resolution method is proposed to significantly reduce the computational complexity of iterative super-resolution algorithms without loss of the desired perceptual quality. A perceptually significant constrained set of active pixels is selected for processing by the SR algorithm based on a just noticeable distortion threshold model. These selected active pixels are further reduced by using saliency information that is determined by a visual attention model. Furthermore, the active pixels lying in the attended regions are processed at a higher accuracy by the SR method relative to pixels in other regions. Simulation results are presented to show the preserved desired visual quality and a 30-40% reduction in complexity over a highly efficient Selective Perceptual Fast Two-Step (SELP-FTS) scheme.