Geometry simplification, or defeaturing, is essential for industrial simulations. It simplifies the meshing process and reduces the computational complexity of a simulation. The former is critical in the context of Isogeometric Analysis (IGA), as creating three-dimensional meshes for IGA can be challenging. Standard defeaturing methods typically use geometric criteria, ignoring the problem's physics. Analysis-aware defeaturing addresses this through a posteriori error estimation, combining the defeatured simulation output and the exact geometry information to guide the defeaturing process. This work presents reliable a posteriori defeaturing error estimators for negative features subject to Dirichlet boundary conditions in Poisson problems.