We present a simple analytical model for the acceleration of low energy electron bunches in the wakefield created by a short laser pulse focused in a uniform plasma. Laser intensity is limited to I~10^18W/cm^2 in order to avoid self-injection and strong nonlinear effects. In this weakly nonlinear regime, it is found that the quality of the accelerated electron bunch—in terms of bunch length and energy spread—depends crucially on the injection energy. Comparisons with numerical simulations show that most of the features of the acceleration process can be explained within the linear response framework, including both the reduction of energy spread and bunch length at low injection energies. The role of nonlinear effects is discussed.