Generalized end-to-end (GE2E) model is widely used in speaker verification (SV) fields due to its expandability and generality regardless of specific languages. However, the long-short term memory (LSTM) based on GE2E has two limitations: First, the embedding of GE2E suffers from vanishing gradient, which leads to performance degradation for very long input sequences. Secondly, utterances are not represented as a properly fixed dimensional vector. In this paper, to overcome issues mentioned above, we propose a novel framework for SV, end-to-end trainable self-attentive shallow network (SASN), incorporating a time-delay neural network (TDNN) and a self-attentive pooling mechanism based on the self-attentive x-vector system during an utterance embedding phase. We demonstrate that the proposed model is highly efficient, and provides more accurate speaker verification than GE2E. For VCTK dataset, with just less than half the size of GE2E, the proposed model showed significant performance improvement over GE2E of about 63%, 67%, and 85% in EER (Equal error rate), DCF (Detection cost function), and AUC (Area under the curve), respectively. Notably, when the input length becomes longer, the DCF score improvement of the proposed model is about 17 times greater than that of GE2E.