Sensitivity analysis of Markovian models amounts to computing the constants in polynomial functions of a parameter under study. To handle the computational complexity involved, we propose a method for approximate sensitivity analysis of such models. We show that theoretical properties allow us to reason for the present time using just few observations from the past with small loss in accuracy. The computational requirements of our method render sensitivity analysis practicable even for complex Markovian models. We illustrate our method by means of a sensitivity analysis of a real-life Markovian model in the field of infectious diseases.