Systemic neurotoxic insecticides are widely used to control aphid pests worldwide and their potential non-target effects on aphid predators are often unknown. Behavioral responses linked to biological control services are crucial when assessing the compatibility of chemicals with biocontrol organisms. This is particularly relevant for insecticides at low and sublethal concentrations. We studied the acute toxicity and the sublethal effect on the voracity of the generalist predator Harmonia axyridis (Coleoptera: Coccinellidae) caused by the exposure to three systemic insecticides routinely used against aphids. The tested insecticide concentrations were the Lethal Concentration 50% (LC50), 20% (LC20) and 1% (LC1) estimated for the target pest Aphis gossypii (Hemiptera: Aphididae) in a companion study. The survival and the voracity differed among the tested chemicals and concentrations, but only thiamethoxam at LC50 caused a significant predator mortality, and individuals that survived showed a reduced predation rate. The predators showed a density independent functional response after the exposure to most of the insecticide-concentration combinations, while an inverse density dependence of the prey consumption rate was observed for coccinellids exposed to sulfoxaflor and thiamethoxam at their lowest tested concentration. The estimated parameters, i.e., the attack rate and the prey handling time, were affected at higher concentrations by both imidacloprid and sulfoxaflor. These findings stress the importance of carefully evaluating side effects of insecticides at very low concentrations on beneficial arthropods in the risk assessment schemes for sustainable pest control programmes.