Defeaturing is a popular CAD/ CAE simplification technique where ‘small or irrelevant features’ are suppressed within a CAD model for speeding-up downstream processes, especially finite element analysis. Unfortunately, defeaturing also results in analysis errors that are not easily quantifiable within the current theoretical framework. In this paper, we provide a rigorous theory for swiftly computing such defeaturing-induced engineering analysis errors. In particular, we focus on problems where the features being suppressed are cutouts of arbitrary shape and size within the body. The proposed theory combines two concepts, namely, adjoint formulation and monotonicity analysis, to arrive at strict bounds on engineering analysis errors when such features are suppressed. The theory is illustrated through numerical examples.