All participants in educational relations are worried about the problem how to improve the quality of education, with everyone representing it through the prism of their value system. In this connection there is a need to structure these representations. It is necessary to begin with bringing into a unified system the representations of education direct customers – students. The aim of our article is to analyze how pedagogical university students perceive the quality of their education. On the basis of the survey involving 117 respondents from Elabuga Institute of Kazan Federal University (Elabuga, Republic of Tatarstan) and the Northeast Federal University named after M.K. Ammosov (Yakutsk, Republic of Sakha (Yakutia)) we analyzed such criteria as quality of teaching, quality of learning, formation of universal competencies, personal qualities necessary for modern teachers and the creation of appropriate conditions by a university (digitalization of the educational environment, academic mobility) for students’ self-development. The t-Student criterion was used to determine the differences between the respondents’ competencies, knowledge, abilities, skills and qualities that they had possessed before entering the university and those that were formed during the university study. The obtained data indicate a high assessment of the quality of education by the students. The results also showed the educational process strong and weak points that students of the two federal universities face. Thus, focusing on one of the customers’ (students’) views will allow teachers to manage the educational process effectively and improve its quality.