Cracks in concrete are common defects that may enable rapid deterioration and failure of structures. Determination of a crack's depth using surface wave transmission measurement and the cut-off frequency in the transmission function (TRF) is difficult, in part due to variability of the measurement data. In this study, use of complete TRF data as features for crack depth assessment is proposed. A principal component analysis (PCA) is employed to generate a basis for the measured TRFs for various simulated crack (notch) cases in concrete. The measured TRFs are represented by their projections onto the most significant PCs. Then neural networks (NN), using the PCA-compressed TRFs, are applied to estimate the crack depth. An experimental study is carried out for five different artificial crack (notch) cases to investigate the effectiveness of the proposed method. Results reveal that the proposed method can effectively estimate the artificial crack depth in concrete structures, even with incomplete NN training.