The current study aimed to investigate how parents of children, adolescents, and young adults with DM1 perceived quality of life and psychological burden during the lockdown period of COVID-19. A cross-sectional study was carried out on 110 parents in Greece in spring 2021. Perceived quality of life was measured using the Parent Diabetes Distress Scale, and psychological burden was measured using the Spielberger State/Trait Anxiety Inventory, and both were assessed with correlational analysis. Overall, 79.1% of the parents were females ,while the mean age of all was 44.4 years (±5.8). PDDS was found to be moderate (mean 2.42 ± 0.76): 63.6% of respondents had moderate/high distress. The highest mean score was for Teen Management Distress and the lowest for Healthcare Team (3.02 vs. 1.49, p < 0.001). STAI was found to be moderate to high, with a higher mean score for state versus trait anxiety (49.8 vs. 48.0, p = 0.006). Increased distress or poorer parents’ quality of life was related with the highest number of hyperglycemic episodes (β = 0.25, p = 0.002), the fewest hypoglycemic episodes (β = −0.18, p = 0.024), and the highest parental trait anxiety (β = 0.04, p < 0.001). Parents were found with moderate-to-high distress and anxiety, and their correlation also shows that there is an urgent need for suitable education of parents on managing the disease to improve quality of life and eliminate health risks to all involved.