Computer-aided segmentation methods can assist medical personnel in improving diagnostic outcomes. While recent advancements like UNet and its variants have shown promise, they face a critical challenge: balancing accuracy with computational efficiency. Shallow encoder architectures in UNets often struggle to capture crucial spatial features, leading in inaccurate and sparse segmentation. To address this limitation, we propose a novel \underline{P}rogressive \underline{A}ttention based \underline{M}obile \underline{UNet} (\underline{PAM-UNet}) architecture. The inverted residual (IR) blocks in PAM-UNet help maintain a lightweight framework, while layerwise \textit{Progressive Luong Attention} ($\mathcal{PLA}$) promotes precise segmentation by directing attention toward regions of interest during synthesis. Our approach prioritizes both accuracy and speed, achieving a commendable balance with a mean IoU of 74.65 and a dice score of 82.87, while requiring only 1.32 floating-point operations per second (FLOPS) on the Liver Tumor Segmentation Benchmark (LiTS) 2017 dataset. These results highlight the importance of developing efficient segmentation models to accelerate the adoption of AI in clinical practice.