Estimating the confidence of disparity maps inferred by a stereo algorithm has become a very relevant task in the years, due to the increasing number of applications leveraging such cue. Although self-supervised learning has recently spread across many computer vision tasks, it has been barely considered in the field of confidence estimation. In this paper, we propose a flexible and lightweight solution enabling self-adapting confidence estimation agnostic to the stereo algorithm or network. Our approach relies on the minimum information available in any stereo setup (i.e., the input stereo pair and the output disparity map) to learn an effective confidence measure. This strategy allows us not only a seamless integration with any stereo system, including consumer and industrial devices equipped with undisclosed stereo perception methods, but also, due to its self-adapting capability, for its out-of-the-box deployment in the field. Exhaustive experimental results with different standard datasets support our claims, showing how our solution is the first-ever enabling online learning of accurate confidence estimation for any stereo system and without any requirement for the end-user.