Using 385 fb^-1 of e^+e^- collision data collected at center-of-mass energies around 10.6 GeV, we search for time-integrated CP violation in the singly Cabibbo-suppressed decays D0/D0bar --> pi^- pi^+ pi^0 and D0/D0bar --> K^- K^+ pi^0. Our model-independent and model-dependent analyses show no evidence of CP violation in these decays. The intermediate amplitudes include well-defined flavor states [e.g., rho(770)^+- pi^-+, K*(892)^+- K^-+] and CP-odd eigenstates [e.g., rho(770)^0 pi^0, phi(1020) pi^0]. With the null results of the previous analyses for CP-even eigenstates D0/D0bar --> K^+ K^- and D0/D0bar --> pi^+ pi^-, we conclude that any CP violation in the singly Cabibbo-suppressed charm decays occurs at a rate which is not larger than a few percent. These results are in accord with the Standard Model predictions, and provide constraints on some models beyond the Standard Model.