The current trend in remote sensing image superresolution (SR) is to use supervised deep learning models to effectively enhance the spatial resolution of airborne and satellite-based optical imagery. Nonetheless, the inherent complexity of these architectures/data often makes these methods very difficult to train. Despite these recent advances, the huge amount of network parameters that must be fine-tuned and the lack of suitable high-resolution remotely sensed imagery in actual operational scenarios still raise some important challenges that may become relevant limitations in existent Earth observation data production environments. To address these problems, we propose a new remote sensing SR approach that integrates a visual attention mechanism within a residual-based network design in order to allow the SR process to focus on those features extracted from land-cover components that require more computations to be super-resolved. As a result, the network training process is significantly improved, because it aims at learning the most relevant high-frequency information while the proposed architecture allows neglecting the low-frequency features extracted from spatially uninformative Earth surface areas by means of several levels of skip connections. Our experimental assessment, conducted using the UC Merced and GaoFen-2 remote sensing image collections, three scaling factors, and eight different SR methods, demonstrates that our newly proposed approach exhibits competitive performance in the task of super-resolving remotely sensed imagery.