The COVID-19 pandemic caused higher education institutions to switch to online learning. This unique endeavor is being investigated to protect high-quality education. Due to its hasty and emergency implementation, students may have different opinions about this new education system. The primary objective of this study is to investigate the relationships between constructs such as students’ perceived effectiveness, institutional facility, teaching material, and overall satisfaction during the COVID-19 outbreak. Adopting a quantitative research approach, this study was conducted between November 8, 2020, and February 12, 2021, in private universities in Bangladesh. Data were utilized in structural equation modeling (SEM). The findings revealed that perceived effectiveness (0.68, p-value = 0.01), institutional facility (0.23, p-value = 0.01), and teaching material (0.14, p-value = 0.01) are all positively and significantly associated with satisfaction with an online class module. In addition, trajectory analysis establishes a link between satisfaction and effectiveness in e-learning through the SEM. The results of the study also indicate a strong and positive correlation between satisfaction with an online class module and perceived effectiveness, institutional setting, and teaching material. This study will serve as a catalyst for understanding students’ satisfaction in an online environment, as well as a benchmark for various stakeholders, particularly policymakers, practitioners, academicians, and institution owners, to take the necessary steps to ensure a sustainable online learning platform.