This paper presents a theoretical and computational method for calculating excitonic polarons and self-trapped excitons from first principles, without requiring supercell calculations. The method combines the many-body Bethe-Salpeter approach with density-functional perturbation theory. It expresses the wavefunction of the excitonic polaron as a coherent superposition of finite-momentum excitons and recasts the BSE total energy functional as a self-consistent eigenvalue problem in the exciton coefficients. The method also provides the accompanying atomic displacements and their spectral decomposition into normal vibrational modes, offering a detailed picture of the excitonic polaron and the atomic-scale mechanisms that drive its formation. The method is demonstrated for the halide double perovskite $ Cs_{2}ZrBr_{6} $, which exhibits signatures of exciton self-trapping. The results show that the excitonic polaron is highly localized, with charge densities localized in real space. The formation energy of the excitonic polaron is significantly smaller than that of the electron and hole polarons, indicating a weaker interaction with the lattice. The excitonic polaron is formed due to the combined effect of electron-phonon and hole-phonon couplings, which partially cancel each other out, leading to a smaller stabilization of the free exciton. The method allows for the identification of the phonon modes responsible for the formation of the excitonic polaron. The dominant contributions come from the $ A_{1g} $ mode at 23.2 meV and the $ T_{1u} $ mode at 6.2 meV. The results show that the excitonic polaron has a more diffuse charge density compared to the electron and hole polarons, indicating a weaker localization. The method is computationally efficient and can be applied to both small and large excitonic polarons as well as self-trapped excitons. This work provides a new approach for investigating the physics of exciton-phonon couplings and self-trapped excitons in diverse classes of materials with potential for solar energy harvesting, photocatalysis, energy-efficient lighting, and light-driven quantum matter.This paper presents a theoretical and computational method for calculating excitonic polarons and self-trapped excitons from first principles, without requiring supercell calculations. The method combines the many-body Bethe-Salpeter approach with density-functional perturbation theory. It expresses the wavefunction of the excitonic polaron as a coherent superposition of finite-momentum excitons and recasts the BSE total energy functional as a self-consistent eigenvalue problem in the exciton coefficients. The method also provides the accompanying atomic displacements and their spectral decomposition into normal vibrational modes, offering a detailed picture of the excitonic polaron and the atomic-scale mechanisms that drive its formation. The method is demonstrated for the halide double perovskite $ Cs_{2}ZrBr_{6} $, which exhibits signatures of exciton self-trapping. The results show that the excitonic polaron is highly localized, with charge densities localized in real space. The formation energy of the excitonic polaron is significantly smaller than that of the electron and hole polarons, indicating a weaker interaction with the lattice. The excitonic polaron is formed due to the combined effect of electron-phonon and hole-phonon couplings, which partially cancel each other out, leading to a smaller stabilization of the free exciton. The method allows for the identification of the phonon modes responsible for the formation of the excitonic polaron. The dominant contributions come from the $ A_{1g} $ mode at 23.2 meV and the $ T_{1u} $ mode at 6.2 meV. The results show that the excitonic polaron has a more diffuse charge density compared to the electron and hole polarons, indicating a weaker localization. The method is computationally efficient and can be applied to both small and large excitonic polarons as well as self-trapped excitons. This work provides a new approach for investigating the physics of exciton-phonon couplings and self-trapped excitons in diverse classes of materials with potential for solar energy harvesting, photocatalysis, energy-efficient lighting, and light-driven quantum matter.