The fundamental requirements for regeneration are poorly understood. Planarians can robustly regenerate all tissues after injury, involving stem cells, positional information, and a set of cellular and molecular responses collectively called the "missing tissue" or "regenerative" response. follistatin, which encodes an extracellular Activin inhibitor, is required for the missing tissue response after head amputation and for subsequent regeneration. We found that follistatin is required for the missing tissue response regardless of the wound context, but causes regeneration failure only after head amputation. This head regeneration failure involves follistatin-mediated regulation of Wnt signaling at wounds and is not a consequence of a diminished missing tissue response. All tested contexts of regeneration, including head regeneration, could occur with a defective missing tissue response, but at a slower pace. Our findings suggest that major cellular and molecular programs induced specifically by large injuries function to accelerate regeneration but are dispensable for regeneration itself.