This work studies an ultra-reliable and low-latency communications (uRLLC) downlink system using pinching antennas which are realized by activating small dielectric particles along a dielectric waveguide. Our goal is to maximize the data rate by optimizing the positions of the pinching antennas. By proposing a compact and cost-efficient antenna architecture and formulating a finite blocklength-based optimization model, we derive a closed-form solution for the optimal antenna placement under quality-of-service (QoS) and antenna spacing constraints. Meanwhile, a phase-alignment strategy is integrated into the design, enabling coherent signal superposition across the array. Simulation results confirm significant rate improvements over conventional antenna systems while satisfying uRLLC requirements, making the proposed design well-suited for compact and latency-critical future applications.