Segmental longitudinal strain (SLS) of the left ventricle (LV) is an important prognostic indicator for evaluating regional LV dysfunction, in particular for diagnosing and managing myocardial ischemia. Current techniques for strain estimation require significant manual intervention and expertise, limiting their efficiency and making them too resource-intensive for monitoring purposes. This study introduces the first automated pipeline, autoStrain, for SLS estimation in transesophageal echocardiography (TEE) using deep learning (DL) methods for motion estimation. We present a comparative analysis of two DL approaches: TeeFlow, based on the RAFT optical flow model for dense frame-to-frame predictions, and TeeTracker, based on the CoTracker point trajectory model for sparse long-sequence predictions. As ground truth motion data from real echocardiographic sequences are hardly accessible, we took advantage of a unique simulation pipeline (SIMUS) to generate a highly realistic synthetic TEE (synTEE) dataset of 80 patients with ground truth myocardial motion to train and evaluate both models. Our evaluation shows that TeeTracker outperforms TeeFlow in accuracy, achieving a mean distance error in motion estimation of 0.65 mm on a synTEE test dataset. Clinical validation on 16 patients further demonstrated that SLS estimation with our autoStrain pipeline aligned with clinical references, achieving a mean difference (95\% limits of agreement) of 1.09% (-8.90% to 11.09%). Incorporation of simulated ischemia in the synTEE data improved the accuracy of the models in quantifying abnormal deformation. Our findings indicate that integrating AI-driven motion estimation with TEE can significantly enhance the precision and efficiency of cardiac function assessment in clinical settings.