Intentional binding is the perceived shortening of the time between a voluntary action and its consequent effect and has been suggested as an implicit measure of agency. This shortening has been linked to processes underlying action preparation and is also affected by post-movement feedback. Intentional binding has been demonstrated in joint action tasks involving two humans, but it is unknown whether it occurs for tasks involving a human working alongside a non-human partner. This experiment investigated the influence of high-level feedback on the experience of agency and whether binding occurs in human-computer joint action settings. Participants were involved in two versions an action task involving another 'agent'. In one version, two participants (a genuine participant and a confederate) sat side by side, separated by a curtain that prevented vision of the other person. In baseline conditions, both participants were instructed to make a self-paced action and judge the time of the action by reporting the position of a rotating clock-hand on a computer screen. In other baseline conditions, participants judged the time of an auditory tone. In operant conditions, participants made actions and the genuine participant's action was followed 200 ms later by a tone on every trial. To examine the effect of post-movement information on binding and explicit agency judgments, a colour cue was presented on each trial informing participants about which person's action caused the tone. In another version of the task, participants were paired with a computer instead of a human co-actor. Post-movement information affected the genuine participant's explicit agency judgments but had no effect on intentional binding, which always occurred. In the human-computer version, participants never showed binding, even when they explicitly judged that their action had caused the tone. We suggest that human-human partnerships result in the formation of a new 'we' agentic identity, but that human-computer partnerships lead to inhibition of the processes that mediate the pre-reflective sense of agency.