By combining the asymptotic correction scheme of Casida and Salahub for exchange-correlation potentials and the phenomenological linear correlation between experimental ionization potentials and highest occupied Kohn-Sham (KS) orbital energies found by Zhan, Nichols, and Dixon, we propose a new, expedient, and self-contained asymptotic correction to exchange-correlation potentials in KS density functional theory (DFT) for use in time-dependent density functional theory (TDDFT) that does not require an ionization potential as an external parameter from a separate calculation. The asymptotically corrected (TD)DFT method is implemented in the quantum chemistry program suite NWChem for both sequential and massively parallel execution. The asymptotic correction scheme combined with the B3LYP functional [B3LYP(AC)] is shown to be well balanced for both valence- and Rydberg-type transitions, with average errors in excitation energies of CO, N-2, CH2O, and C2H4 being smaller than those of uncorrected BLYP and B3LYP TDDFT by factors of 4 and 2, respectively, consistent with the improved orbital energies found for B3LYP(AC). We demonstrate the general applicability and accuracy of the method for the Rydberg excited states of mono- to tetrafluorinated methanes, the valence and Rydberg excited states of benzene, and the Q, B, N, and L band positions of free-base porphin.