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Twisted moiré lattices (TMLs) are superlattices that usually comprise two identical two-dimensional lattices with a relative twist angle. Depending on the twist angle, periodic and aperiodic patterns are afforded. Recently, flat bands and localized states have been achieved in photonic and phononic TMLs with periodic patterns. However, the physics of phononic TMLs with quasicrystalline patterns still need to be determined. In this Letter, we theoretically and experimentally realize point- and loop-shaped localized states induced by the flat bands in phononic TMLs with quasicrystalline patterns. The flat bands in our phononic TML do not occur due to the hybridization of the bands near the Dirac point. They evolve from the trivial bands; trivial bands flatten in wide bandgaps due to strong interlayer couplings, yielding flat bands. As the average group velocity of flat bands can be extremely close to zero, the localized states can be bounded in the moiré points and the moiré loops of phononic TMLs with quasicrystalline patterns. Our findings provide a method for manipulating classical waves in various moiré structures with quasicrystalline patterns.