The vulnerability of Automatic Speaker Verification (ASV) systems to spoofing or presentation attacks is still an open security issue. In this context, replay spoofing attacks pose a great threat to an ASV system since they can be easily performed (using a playback device, and without needing any technical skill). In this paper, we analyze replay speech signals in terms of reverberation that may occur during recording of the speech signal. Such reverberation introduces delay and changes in amplitude, producing close copies of speech signals, which significantly influences the replay components. To that effect, we propose to exploit the capabilities of the Teager Energy Operator (TEO) to compute a running estimate of subband energies for replay vs. genuine signals. We have used a linearly-spaced Gabor filterbank to obtain a narrowband filtered signal. The TEO has the ability to track the instantaneous changes of a signal. Experiments are performed on the ASVspoof 2017 Challenge version 2.0 database using a Gaussian Mixture Model (GMM) as pattern classifier. Furthermore, we compared our results with state-of-the-art feature sets, namely, Constant Q Cepstral Coefficients (CQCC), Linear Frequency Cepstral Coefficients (LFCC), Mel Frequency Cepstral Coefficients (MFCC), and used their score-level fusion with the proposed feature sets, i.e., Teager Energy Cepstral Coefficients (TECC), in order to obtain possible complementary information that further reduces the Equal Error Rate (EER). Relatively low EERs are obtained with score-level fusion of CQCC, MFCC, LFCC, and TECC feature sets, resulted in 6.68% and 10.45% on development and evaluation sets, respectively. Moreover, for the evaluation dataset, we also studied the performance of the TECC feature set on different Replay Configurations (RC), namely, for acoustic environments, playback, and recording devices. For all the levels of threat conditions (i.e., low, medium, and high-level) to an ASV system, the proposed feature set performed better compared to existing state-of-the-art feature sets. In addition to the ASVspoof 2017 Challenge database, we also performed experiments on other spoofing databases, namely, the ASVspoof 2015 Challenge, BTAS 2016, and ASVspoof 2019 Challenge databases. For all the spoofing databases used in this study, the proposed TECC feature set perform significantly better than the other feature sets.