This work investigates the extension of the Controlled Lagrangians methodology for underactuated mechanical systems subject to matched and unmatched disturbances. A new passivity-preserving controller design that includes two dynamic extensions for disturbance rejection purposes is presented. The new controller is compared with the corresponding port-controlled Hamiltonian implementation, and an interpretation of the dynamic extensions as low-pass filters is proposed. The effectiveness of the proposed controller is demonstrated with numerical simulations.