Students' feedback assessment became a hot topic in recent years with growing e-learning platforms coupled with an ongoing pandemic outbreak. Many higher education institutes were compelled to shift on-campus physical classes to online mode, utilizing various online teaching tools and massive open online courses (MOOCs). For many institutes, including both teachers and students, it was a unique and challenging experience conducting lectures and taking classes online. Therefore, analyzing students' feedback in this crucial time is inevitable for effective teaching and monitoring learning outcomes. Thus, in this paper, we propose and conduct a study to evaluate various machine learning models for aspect-based opinion mining to address this challenge effectively. The proposed approach is trained and validated on a large-scale dataset consisting of manually labeled students' comments collected from the Coursera online platform. Various conventional machine learning algorithms, namely Random Forest (RF), Support Vector Machine (SVM), and Decision Tree (DT), along with deep-learning methods, are employed to identify teaching-related aspects and predict opinions/attitudes of students towards those aspects. The obtained results are very promising, with an F1 score of 98.01% and 99.43% achieved from RF on the aspect identification and the aspect sentiment classification task, respectively.