The possibility of studying non-thermal electron energization in laser-driven plasma experiments of magnetic reconnection is studied using two- and three-dimensional particle-in-cell simulations. It is demonstrated that non-thermal electrons with energies more than an order of magnitude larger than the initial thermal energy can be produced in plasma conditions currently accessible in the laboratory. Electrons are accelerated by the reconnection electric field, being injected at varied distances from the X-points, and in some cases trapped in plasmoids, before escaping the finite-sized system. Trapped electrons can be further energized by the electric field arising from the motion of the plasmoid. This acceleration gives rise to a non-thermal electron component that resembles a power-law spectrum, containing up to ~ 8% of the initial energy of the interacting electrons and ~ 24% of the initial magnetic energy. Estimates of the maximum electron energy and of the plasma conditions required to observe suprathermal electron acceleration are provided, paving the way for a new platform for the experimental study of particle acceleration induced by reconnection. Show Partial Abstract