A fully ab initio method of solution to compute autoionizing states in Li-like atomic systems based on the application of the Feshbach projection formalism is proposed. Applications of the Feshbach formalism, which in principle is a complete many-particle theory, to systems of more than two-active electrons are very scarce due to the limitations imposed by the practical construction of correct projection operators and inherent to the theory. We include rigorously all the ingredients required by the Feshbach theory in order to compute accurate resonance parameters for the lowest autoionizing states of Li and Ne7+, for the 2Se, 2P° and 2De symmetries.