Centrality dependence of the directed flow of protons in Au+Au collisions at the beam energy of 1.23A GeV collected by the HADES experiment at GSI is presented. Measurements are performed with respect to the spectators plane estimated using the Forward Wall hodoscope. Biases due to non-flow correlations and correlated detector effects are evaluated. The corresponding systematic uncertainties are quantified using estimates of the spectators plane from various forward rapidity regions constructed from groups of Forward Wall channels and protons reconstructed with the HADES tracking system.