Jet quenching is the process of color-charged partons losing energy via interactions with quark-gluon plasma droplets created in heavy-ion collisions. The collective expansion of such droplets is well described by viscous hydrodynamics. Similar evidence of collectivity is consistently observed in smaller collision systems, including pp and p+Pb collisions. In contrast, while jet quenching is observed in Pb+Pb collisions, no evidence has been found in these small systems to date, raising fundamental questions about the nature of the system created in these collisions. The ATLAS experiment at the Large Hadron Collider has measured the yield of charged hadrons correlated with reconstructed jets in 0.36 nb^{-1} of p+Pb and 3.6 pb^{-1} of pp collisions at 5.02 TeV. The yields of charged hadrons with p_{T}^{ch}>0.5 GeV near and opposite in azimuth to jets with p_{T}^{jet}>30 or 60 GeV, and the ratios of these yields between p+Pb and pp collisions, I_{pPb}, are reported. The collision centrality of p+Pb events is categorized by the energy deposited by forward neutrons from the struck nucleus. The I_{pPb} values are consistent with unity within a few percent for hadrons with p_{T}^{ch}>4 GeV at all centralities. These data provide new, strong constraints that preclude almost any parton energy loss in central p+Pb collisions.