Mastery of generic competences is widely recognized as important for a successful transition from higher education to the world of work, especially in today's networked, digitalized, and globalized environment. This study analyses data of 7201 respondents to the Croatian national graduate survey 2017 on students who graduated in the academic year 2015/2016 in different fields of education (Medicine and Biomedical Sciences, Biotechnical Sciences, Social Sciences, Humanities, Natural Sciences, Technical Sciences and Arts). The goal of this study is to identify graduates' perspectives on gaps between the generic and digital competences acquired during higher education studies and those required in the first workplace. It addresses three research questions: (1) Which generic and digital competences do graduates consider relevant for employability?, (2) Which groups of competences show a similar pattern of competence gap, from the graduate's perspective?, and (3) How do graduates' perceptions of gaps in competence levels vary among fields of education? Research results reveal disparities in graduates' perceptions about achieved competence levels and labour market requirements. The study identifies differences among graduates from different fields of education. Results may be useful to educators in all fields of education as guidelines for the introduction of generic and digital competences development in higher education.