Plexcitonic nanoparticles exhibit strong light‐matter interactions, mediated by localized surface plasmon resonances, and thereby promise potential applications in fields such as photonics, solar cells, and sensing, among others. Herein, these light‐matter interactions are investigated by UV‐visible and surface‐enhanced Raman scattering (SERS) spectroscopies, supported by finite‐difference time‐domain (FDTD) calculations. Our results reveal the importance of combining plasmonic nanomaterials and J‐aggregates with near‐zero‐refractive index. As plexcitonic nanostructures nanorattles are employed, based on J‐aggregates of the cyanine dye 5,5,6,6‐tetrachloro‐1,1‐diethyl‐3,3‐bis(4‐sulfobutyl)benzimidazolocarbocyanine (TDBC) and plasmonic silver‐coated gold nanorods, confined within mesoporous silica shells, which facilitate the adsorption of the J‐aggregates onto the metallic nanorod surface, while providing high colloidal stability. Electromagnetic simulations show that the electromagnetic field is strongly confined inside the J‐aggregate layer, at wavelengths near the upper plexcitonic mode, but it is damped toward the J‐aggregate/water interface at the lower plexcitonic mode. This behavior is ascribed to the sharp variation of dielectric properties of the J‐aggregate shell close to the plasmon resonance, which leads to a high opposite refractive index contrast between water and the TDBC shell, at the upper and the lower plexcitonic modes. This behavior is responsible for the high SERS efficiency of the plexcitonic nanorattles under both 633 nm and 532 nm laser illumination. SERS analysis showed a detection sensitivity down to the single‐nanoparticle level and, therefore, an exceptionally high average SERS intensity per particle. These findings may open new opportunities for ultrasensitive biosensing and bioimaging, as superbright and highly stable optical labels based on the strong coupling effect.