Understanding the effect of the material parameter variability on the mechanical response of laminated composites is of great importance in non-linear Finite Element (FE) applications and in many engineering problems. Not only an accurate sensitivity analysis enables to estimate how much each parameter under consideration affects the response, but the linearization of the output provides also the possibility to propagate in an inexpensive way the material uncertainties, hence resulting useful in the context of Uncertainty Quantification and Propagation employing stochastic perturbation techniques. This is particularly important in simulations concerning laminated composite materials using up-to-date damage models which often lead to computationally intensive simulations. In this paper, a material parameter sensitivity study is carried out in the context of continuum damage mechanics applied to laminated composites. The sensitivity w.r.t. the input material variables is estimated in an inexpensive way from a single run of the FE model using the so-called Direct Differentiation Method (DDM). The material parameters include elastic moduli, strengths and fracture toughnesses. A semi-analytical approach was used, rendering much simpler the implementation in a FE code. For a more precise computation, the Complex Step Differentiation (CSD) method was employed. Furthermore, in order to reduce even more the computational cost, the DDM was implemented as a post-processing step using a reduced number of time increments. The obtained results show that the linearization carried out allow to estimate relatively well the reaction force developed by some specimens under tension as the material parameters change their values and to follow the weight of each parameter on the mechanical response during the load history.