This paper aims to determine the perception of small and medium-sized enterprises (SMEs) employees regarding the usage of cloud computing services in their activities. The quantitative study was conducted on a sample of 315 respondents employed in Romanian SMEs. Testing of the conceptual model was performed with the WarpPLS 3.0 software. The study aimed to test how several constructs—the perceived benefits, disadvantages and risks, communication process, overall experience of using cloud computing services, perceived image, and empathy regarding the cloud computing services—influence the perception of the cloud computing service quality among SMEs employees. Moreover, employees’ perception regarding the satisfaction of using cloud computing services based on the perceived quality was also tested. We concluded that the perceived benefits and disadvantages of cloud computing service usage, the perception of both the communication process and users’ experience regarding cloud computing service use, empathy, and cloud computing service image positively influence the perceived quality of the cloud computing service usage in SMEs. We did not find evidence that the perceived risks significantly influence the perceived quality of cloud computing services. Finally, we demonstrated that the perceived quality of the cloud computing services positively influences the satisfaction regarding cloud computing services among SMEs employees.