The paper is an attempt to remove incongruencies between predictions of the mean-field approximation to the classic Lotka-Volterra model and recent Monte Carlo simulations of the stochastic two-species predator-prey reaction systems on regular lattices. To this end the Doi-Peliti path integral representation of the master equation for stochastic interacting particle systems has been invoked. The field theory action has been derived in the continuum limit. Links with the Reggeon field theory and the universal scaling behavior of critical directed percolation clusters have been employed. A perturbative loop expansion with respect to the predation rate allows to demonstrate that instabilities in the structure formation are induced. The downward renormalization of the population oscillation frequency and the diffusion coefficient are found to stay in a qualitative agreement with Monte Carlo simulations started from random initial states.