Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of T-periodic solutions lying inside a bounded domain Omega subset of R-N is, generically, at least vertical bar chi +/- 1 vertical bar + 1, where chi denotes the Euler characteristic of Omega. Moreover, some connections between the associated fixed point operator and the Poincare operator are explored.