We study the sensitivity of future xenon-and argon-based dark matter and neutrino detection experiments to low-energy atmospheric neutrinos. Not accounting for experimental backgrounds, the primary obstacle for identifying nuclear recoils induced by atmospheric neutrinos in xenon is the tail of the electron recoil distribution due to pp solar neutrinos. We use the NEST code to model the solar and atmospheric neutrino signals in a xenon detector and find that an exposure of 700 tonne-years will produce a 5σ detection of atmospheric neutrinos. We explore the effect of different detector properties and find that a sufficiently long electron lifetime is essential to the success of such a measurement.