The British pairing were beaten 6-1, 6-4, by Neal Skupski and Desirae Krawcryk.
Watson and Salisbury were alternates in the competition, and had beaten Rafael Matos and Luisa Stefani (6-3, 6-4) in the first round before moving past number eight seeds Jean-Julien Rojer and Ellen Perez (6-3, 6-2) in the second round.