The fundamental problems with component production in the automotive industry are the low quality of the components, the high number of failures, and the subsequent number of complaints. The quality of automotive components is a prerequisite for automated production in a SMART Factory 4.0 in the context of Industry 4.0. Managing complaints is a critical area in the automotive manufacturing industry. The primary goal of this article is to indicate the significance of a CRM system and the importance of complaints management in automotive manufacturing, which improves the quality of the process of producing components while improving the quality of the inputs—the quality of materials, the quality of the human factor, and the quality of the services provided in connection with the components. (1) A Slovak company was selected as the subject of this research, which focuses on the production of automotive parts. (2) The methods of research focused on using economic analysis and instruments of quality management such as the QRQC method, FMEA method, the Ishikawa diagram, and the Pareto analysis and Lorenz curve. This article presents the results of complaints about automotive components: locksets in vehicles. (3) This research shows the basic cause of the problem: a bent pin after riveting in the process of producing the components. In the frame of this research, we suggested corrective measures to eliminate the actual causes of failure in the production of the components. The RPN index reached a level below the limit of 150 (the critical level of the customers’ requirements) after implementing the corrective measures. The total costs of complaints in this year were calculated to be EUR 13.575 and the costs will be reduced gradually after changes are implemented in the production process. (4) A new complaints information system and a new training center are beneficial for solving problems in the production of automotive components. The implementation of a CRM system and other systems are prerequisites for solving customer complaints.