This letter investigates an acoustic metamaterial exhibiting a unique sound pressure amplification mechanism for ultra-low frequency sound attenuation. The system is constructed by integrating a flexible panel into the side-branch duct of a Herschel-Quincke (HQ) tube. A new peak emerges in the Sound Transmission Loss (STL) at a frequency far lower than the frequencies of the HQ tube-induced STL peaks. It cannot, after careful comparisons, be attributed to any local resonances, including structural resonances of the flexible panel or air resonances inside the side-branch cavities. To explain the underlying physics, several numerical simulations are performed. The results reveal that analog to a mechanical inerter, a "push-pull" force is created by the sound pressure difference between the sub-cavities in which a pressure amplification mechanism is generated at the interface of the embedded panel. This force is large enough to activate an out-of-plane motion of the flexible panel, trapping the incident sound power in a circular flow around the duct-branch loop. The unique phenomenon is successfully reproduced in experiment, where the flexible panel is made of carbon fiber. The proposed acoustic metamaterial can be used as silencing components for ultra-low frequency noise control in duct.