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Several recent studies have demonstrated the promise of deep visuomotor policies for robot manipulator control. Despite impressive progress, these systems are known to be vulnerable to physical disturbances, such as accidental or adversarial bumps that make them drop the manipulated object. They also tend to be distracted by visual disturbances such as objects moving in the robot’s field of view, even if the disturbance does not physically prevent the execution of the task. In this paper, we propose an approach for augmenting a deep visuomotor policy trained through demonstrations with Task Focused visual Attention (TFA). The manipulation task is specified with a natural language text such as “move the red bowl to the left”. This allows the visual attention component to concentrate on the current object that the robot needs to manipulate. We show that even in benign environments, the TFA allows the policy to consistently outperform a variant with no attention mechanism. More importantly, the new policy is significantly more robust: it regularly recovers from severe physical disturbances (such as bumps causing it to drop the object) from which the baseline policy, i.e. with no visual attention, almost never recovers. In addition, we show that the proposed policy performs correctly in the presence of a wide class of visual disturbances, exhibiting a behavior reminiscent of human selective visual attention experiments.