This paper introduces a goal-oriented error control for the finite cell method (FCM). The FCM is characterized by embedding the physical domain of the problem into a fictitious domain to which the finite element method (FEM) is applied. The error identity is derived by the dual residual (DWR) method and enables the separation of the different error contributions which are introduced by the FCM: discretization, quadrature and fictitious domain. In particular, the additional consideration of the fictitious domain error has a significant impact on the solution process. This is demonstrated in a numerical example.