Objective: To develop a robust and compact deep learning model for automated knee cartilage segmentation on point-of-care ultrasound (POCUS) devices. Methods: We propose MonoUNet, a novel, highly compact segmentation model consisting of (i) an aggressively reduced U-Net backbone, (ii) a trainable monogenic block that extracts multi-scale local phase features from the input, and (iii) a gating mechanism that injects these features into the encoder stages to reduce sensitivity to variations in ultrasound image appearance. MonoUNet segmentation performance was evaluated on a multi-site, multi-device knee cartilage ultrasound dataset using Dice score and mean average surface distance (MASD). Agreement between MonoUNet and manual cartilage outcomes (thickness and echo intensity) was assessed using Bland-Altman analysis with 95% limits of agreement, and reliability was assessed using intraclass correlation coefficient (ICC$_{2,k}$). Results: Overall, MonoUNet outperformed existing lightweight segmentation models, with average Dice scores ranging from 92.62% to 94.82% and MASD values between 0.133 mm and 0.254 mm. MonoUNet reduces the number of parameters by 10x--700x and computational cost by 14x--2000x relative to existing lightweight models. MonoUNet cartilage outcomes showed excellent reliability and agreement with the manual outcomes: intraclass correlation coefficients (ICC$_{2,k})$=0.96 and bias=2.00% (0.047 mm) for average thickness, and ICC$_{2,k}$=0.99 and bias=0.80% (0.328 a.u.) for echo intensity. Conclusion: Incorporating trainable local phase features improves the robustness of highly compact neural networks for knee cartilage segmentation across varying acquisition settings and could support scalable ultrasound-based assessment and monitoring of knee osteoarthritis using POCUS devices. The code is publicly available at https://github.com/alvinkimbowa/monounet.