Unemployment Insurance Technology Modernization Act of 2021 This bill requires the Department of Labor to study and report on the technology needs of federal and state unemployment compensation programs. Based on this study, Labor must develop, operate, and maintain a modular set of technology capabilities to modernize the delivery of unemployment compensation. Before the deployment of the technology capabilities to all states, Labor must select at least four states to participate in a pilot program to test the technology capabilities and demonstrate that they meet requirements. The bill establishes accessibility requirements for filing online unemployment compensation claims. In addition, it prohibits the technology capabilities from relying solely on a high-risk automated decision system to (1) deny a claim for unemployment compensation, (2) reduce the amount of unemployment compensation for which a claimant is eligible, or (3) deny a claimant's right to appeal an unemployment compensation decision.