Social media offers a unique lens to observe large-scale, spatial-temporal patterns of users reactions toward critical events. However, social media use varies across demographics, with younger users being more prevalent compared to older populations. This difference introduces biases in data representativeness, and analysis based on social media without proper adjustment will lead to overlooking the voices of digitally marginalized communities and inaccurate estimations. This study explores solutions to pinpoint and alleviate the demographic biases in social media analysis through a case study estimating the public sentiment about COVID-19 using Twitter data. We analyzed the pandemic-related Twitter data in the U.S. during 2020-2021 to (1) elucidate the uneven social media usage among demographic groups and the disparities of their sentiments toward COVID-19, (2) construct an adjusted public sentiment measurement based on social media, the Sentiment Adjusted by Demographics (SAD) index, to evaluate the spatiotemporal varying public sentiment toward COVID-19. The results show higher proportions of female and adolescent Twitter users expressing negative emotions to COVID-19. The SAD index unveils that the public sentiment toward COVID-19 was most negative in January and February 2020 and most positive in April 2020. Vermont and Wyoming were the most positive and negative states toward COVID-19.