We present an X-ray study of the massive edge-on Sa galaxy, Sombrero (M 104; NGC 4594), based on XMM–Newton and Chandra observations. A list of 62 XMM–Newton and 175 Chandra discrete X-ray sources is provided, the majority of which are associated with the galaxy. Spectral analysis is carried out for relatively bright individual sources and for an accumulated source spectrum. At energies ≳2 keV, the source-subtracted X-ray emission is distributed similarly as the stellar K-band light and is primarily due to the residual emission from discrete sources. At lower energies, however, a substantial fraction of the source-subtracted emission arises from diffuse hot gas extending to ∼20 kpc from the galactic centre. The galactic disc shows little X-ray emission and instead shadows part of the X-ray radiation from the bulge. The observed diffuse X-ray emission from the galaxy shows a steep spectrum that can be characterized by an optically thin thermal plasma with temperatures of ∼0.6–0.7 keV, varying little with radius. The diffuse emission has a total luminosity of ∼3 × 1039 erg s−1 in the 0.2–2 keV energy range. This luminosity is significantly smaller than the prediction by current numerical simulations for galaxies as massive as Sombrero. However, such simulations do not include the effect of quiescent stellar feedback (e.g. ejecta from evolving stars and Type Ia supernovae) against the accretion from intergalactic medium. We argue that the stellar feedback likely plays an essential role in regulating the physical properties of hot gas. Indeed, the observed diffuse X-ray luminosity of Sombrero accounts for at most a few per cent of the expected mechanical energy input from Type Ia supernovae. The inferred gas mass and metal content are also substantially less than those expected from stellar ejecta. We speculate that a galactic bulge wind, powered primarily by Type Ia supernovae, has removed much of the ‘missing’ energy and metal-enriched gas from the region revealed by the X-ray observations.