In this article, we perform the symmetry analysis of perovskite-based multiferroics: bismuth ferrite (BiFeO3)-like, orthochromites (RCrO3), and Ruddlesden-Popper perovskites (Ca3Mn2O7-like), being the typical representatives of multiferroics of the trigonal, rhombic, and tetragonal crystal families and explore the effect of crystallographic distortions on magnetoelectric properties. We determine the principal order parameters for each of the considered structures and obtain their invariant combinations consistent with the particular symmetry. This approach allowed us to analyze the features of the magnetoelectric effect observed during structural phase transitions in BixR1-xFeO3 compounds and show that the rare-earth sublattice gives an impact into the linear magnetoelectric effect allowed by the symmetry of the new structure. It is shown that the magnetoelectric properties of ortho-chromites are attributed to the couplings between the magnetic and electric dipole moments arising near Cr3+ ions due to distortions linked with rotations and deformations of the CrO6 octahedra. For the first time, such symmetry consideration was implemented in the analysis of the Ruddlesden-Popper structures, which demonstrates the possibility of realizing the magnetoelectric effect in the Ruddlesden-Popper phases containing magnetically active cations and allows to estimate conditions required for its optimization.