The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of well-known phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single- and two-photon states in phase space and certify their nonclassicality with high statistical significance.