We perform a reanalysis of the energy levels obtained in a recent lattice QCD simulation, from where the existence of bound states of KD and KD ∗ are induced and identified with the narrow D s0 ∗ (2317) and D s1 ∗ (2460) resonances. The reanalysis is done in terms of an auxiliary potential, employing a single-channel basis KD(∗), and a two-channel basis KD(∗), ηD s (∗) . By means of an extended Lüscher method we determine poles of the continuum t-matrix, bound by about 40 MeV with respect to the KD and KD ∗ thresholds, which we identify with the D s0 ∗ (2317) and D s1 ∗ (2460) resonances. Using a sum rule that reformulates Weinberg compositeness condition we can determine that the state D s0 ∗ (2317) contains a KD component in an amount of about 70%, while the state D s1 ∗ (2460) contains a similar amount of KD ∗. We argue that the present lattice simulation results do not still allow us to determine which are the missing channels in the bound state wave functions and we discuss the necessary information that can lead to answer this question.