The total vaccination rate remains relatively low in Russia as of March 2022 (around 55%, with around 20% in some regions). In the paper, we study the reasons for it. We communicate the results of our survey aimed at detecting reasons for the relatively low anti-SARS-CoV-2 vaccination rate in Russia (47.1% as of mid-January 2022) and suggest potential measures to increase the level of confidence in the Russian vaccination campaign. A total of 14,310 users exhibited interest to participate in the research (16.84% of the total number of invitations sent in the Russian social network VKontakte). After the sample set repair, only 5822 (40.68% of those who agreed to participate) responses were suitable for the research, and they composed the final set. The age range of the respondents was 16–51 years old (y.o.) with a mean of 29.1 ± 10.6 y.o. The proportion of the female gender in responses was 44.23%. A total of 2454 persons (42.15%) expressed their hesitant, cautious, or negative attitude towards vaccine uptake. Of the 2454 persons with cautious attitude towards vaccination, only 928 (37.82%) were concerned about the quality of the Russian vaccines. A total of 1323 individuals (53.91%) supported one or more conspiracy beliefs. A total of 5064 (86.98% of the whole set) showed cautious or negative attitude towards the planned introduction of a nationwide system of vaccination certification/verification based on QR codes. The main social factors that hinder the Russian vaccination campaign are: vexation over the lack of desire of officials to receive feedback from the general population regarding vaccination, wide support for conspiracy beliefs, and controversy over the QR code-based digital system. To elevate the vaccination rate in Russia, the following steps may be taken: social encouragement of those who support vaccination, increase in transparency of the vaccination campaign, acceptance of both digital and paper vaccination certificates, increase in participation of society in vaccination-related discussions, public disclosure of vaccine composition, and avoidance of excessive digitalization of data in the vaccination campaign.