Bundles of filaments and motors are central to contractility in cells. The classic example is striated muscle, where actomyosin contractility is mediated by highly organized sarcomeres which act as fundamental contractile units. However, many contractile bundles in vivo and in vitro lack sarcomeric organization. Here we propose a model for how contractility can arise in bundles without sarcomeric organization and validate its predictions with experiments on a reconstituted system. In the model, internal stresses in frustrated arrangements of motors with diverse velocities cause filaments to buckle, leading to overall shortening. We describe the onset of buckling in the presence of stochastic motor head detachment and predict that buckling-induced contraction occurs in an intermediate range of motor densities. We then calculate the size of the "contractile units" associated with this process. Consistent with these results, our reconstituted actomyosin bundles show contraction at relatively high motor density, and we observe buckling at the predicted length scale.