The relationship between education and work is of the greatest concern to individuals and society because they are the key drivers of growth and development. In the context of Industry 4.0, labor and educators are facing the challenges of big changes in the workplace. How to prepare undergraduate students for the world of employment has become the most important mission of higher education providers. This paper explored the competency gap in the labor market in Vietnam from the perspective of employees who have been dissatisfied with the current status. First, a qualitative method with the Delphi technique was applied to confirm this consensus in an employees' competency model. Then, the satisfaction level for each competency criterion was explored by applying the advance quantitative method, namely, best non-fuzzy performance approach. Lifelong learning was ranked first, followed by creativity and innovation, foreign languages, expertise and digitalization, adaptability, and finally, organizing and managing ability. Critical thinking and problem-solving were perceived to have the biggest gap. The order of competency satisfaction is useful in explaining the mismatch between education quality and labor market demand. The findings provide valuable guidelines for education managers who seek to bridge the competency gap and improve education quality.