Background/Objectives: Coronavirus disease 2019 (COVID-19) course may differ among individuals—in particular, those with comorbidities may have severe pneumonia, requiring oxygen supplementation or mechanical ventilation. Post-COVID-19 long-term structural changes in imaging studies can contribute to persistent respiratory disturbance. This study aimed to investigate COVID-19 sequels affecting the possibility of persistent structural lung tissue abnormalities and their influence on the respiratory function of peripheral airways and gas transfer. Methods: Patients were divided into two groups according to severity grades described by the World Health Organization. Among the 176 hospitalized patients were 154 patients with mask oxygen supplementation and 22 patients with high-flow nasal cannula (HFNC) or mechanical ventilation. All tests were performed at 3, 6, and 9 months post-hospitalization. Results: Patients in the severe/critical group had lower lung volumes in FVC, FVC%, FEV1, FEV1%, LC, TLC%, and DLCO% at three months post-hospitalization. At 6 and 9 months, neither group had significant FVC and FEV1 value improvements. The MEF 25–75 values were not significantly higher in the mild/moderate group than in the severe/critical group at three months. There were weak significant correlations between FVC and FEV1, MEF50, MEF 75, plethysmography TLC, disturbances in DLCO, and total CT abnormalities in the severe/critical group at three months. In a mild/moderate group, there was a significant negative correlation between the spirometry, plethysmography parameters, and CT lesions in all periods. Conclusions: Persistent respiratory symptoms post-COVID-19 can result from fibrotic lung parenchyma and post-infectious stenotic small airway changes not visible in CT, probably due to persistent inflammation.