European universities must face the challenge of diversity and design inclusive practices to address it as part of their social responsibility. However, not all universities are doing the same in terms of diversity practices, so it is important to gather the perceptions of the protagonists. To this end, we have analysed university faculty's perceptions using a mixed model with a concurrent methodological strategy, including an ad hoc questionnaire validated with 880 educators, as well as 17 semi-structured interviews. The triangulation of these two instruments allowed us to analyse three key dimensions associated with the idea of attention to diversity in the university: diversity concept or culture, policies and programmes of the institution, and inclusive educational practices. The conclusion is that the faculty members are positively predisposed to get involved in the process of attention to diversity in all three dimensions, especially in the design of inclusive teaching practices such as the Universal Design of Learning (UDL), although they do point out that it is important to systematise diversity policies in research, innovation, and teaching to keep promoting the social commitment and responsibility of higher education institutions.