The computational effort entailed in the discretization of fluid-poromechanics systems is typically highly demanding. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral anatomy-requiring a very fine computational mesh for finite element discretization-and to the high number of variables involved. Indeed, this kind of problems can be modeled by a coupled system encompassing the Stokes equations for the cerebrospinal fluid in the brain ventricles and Multiple-network Poro-Elasticity (MPE) equations describing the brain tissue, the interstitial fluid, and the blood vascular networks at different space scales. The present work aims to rigorously derive a posteriori error estimates for the coupled Stokes-MPE problem, as a first step towards the design of adaptive refinement strategies or reduced order models to decrease the computational demand of the problem. Through numerical experiments, we verify the reliability and optimal efficiency of the proposed a posteriori estimator and identify the role of the different solution variables in its composition.