Care for the critically ill patients is often considered synonymous with a hospital having an intensive care unit. However, a focus on Essential Emergency and Critical Care (EECC) may obviate the need for much intensive care. Severe COVID-19 presented a specific critical care challenge while also being an exemplar of critical illness in general. Our multidisciplinary team conducted research in Kenya and Tanzania on hospitals' ability to provide EECC as the COVID-19 pandemic unfolded. Important basic inputs were often lacking, especially sufficient numbers of skilled health workers. However, we learnt that higher scores on resource readiness scales were often misleading, as resources were often insufficient or not functional in all the clinical areas they are needed. By following patient journeys, through interviews and group discussions, we revealed gaps in timeliness, continuity and delivery of care. Generic challenges in transitions between departments were identified in the receipt of critically ill patients, the ability to sustain monitoring and treatment and preparation for any subsequent transition. While the global response to COVID-19 focused initially on providing technologies and training, first ventilators and later oxygen, organisational and procedural challenges seemed largely ignored. Yet, they may even be exacerbated by new technologies. Efforts to improve care for the critically ill patients, which is a complex process, must include a whole system and whole facility view spanning all areas of patients' care and their transitions and not be focused on a single location providing 'critical care'. We propose a five-part strategy to support the system changes needed.