During the COVID-19 pandemic, uncertainty, threat to life, and repeated lockdowns have significantly undermined people’s psychological well-being. In such situations, the basic needs for self-determination (SDT) are disrupted—autonomy, connectedness, and competence—but it is the resulting dissatisfaction that actualizes a search for strategies to cope with the problem. The objective of this article is to critically review the literature on various ways that people are coping with specific experiences during the COVID-19 pandemic and their relationship to basic needs to maintain sustainability. We searched on the Web of Science CC database for relevant studies (2020–2021) and their systematization from the standpoint of Self-Determination Theory (SDT). This showed the dynamics of coping methods, reflecting a transition from confusion when confronted with stress, to the selection of effective strategies, confirming that when basic needs are blocked for a long time, people begin to search for a way to satisfy them. We present three levels of grouped coping methods: (1) physiological, (2) behavioral, and (3) cognitive, demonstrating their interrelationship with orientation (to oneself or to the context), assessment (a threat or a challenge), and basic psychological needs. The proposed model opens up prospects for creating effective coping and training programs for sustainable development of the individual in crisis situations.