In addition to teaching and research, the “third mission” has become one of the major societal challenges faced by higher education institutions worldwide. This is related to the university’s efforts to contribute to the economic and social development of the community in which they operate. One of the major concepts focused on this issue is university social responsibility (USR). This study aimed to compare students’ perceptions of and attitude toward USR in two different countries, India and Croatia, and contribute to the research gap in cross-cultural aspects of USR. Since students are the most important stakeholders of the university and today’s students are known as Generation Z–altruistic, caring about the environment and social issues on one hand, and knowing that social responsibility is highly contextual regarding environment—it makes sense to study and compare students from two different countries. The research was conducted at Indian and Croatian universities, with a sample of 1340 respondents. It is based on Carroll’s pyramid of social responsibility regarding levels of USR (economic, legal, ethical, and philanthropic) and the ISO 26000 standards regarding areas of USR. Descriptive statistics, ANOVA, correlation, and regression analysis indicated some differences in perceptions of USR in the two countries but also the significant impact of knowledge about USR and having a course on social responsibility built into the curriculum on perceptions and attitude toward USR. The results show that universities in both countries need to focus on their third mission—specifically, contributing to local community development in creating their USR policies.