The American 19-year-old, who defeated Serena Williams on the way to the last four in Melbourne, went down 5-7 6-3 6-2 to to Romania's Sorana Cirstea in just over two hours.
Former world number one Ana Ivanovic claimed a straight-sets victory over Russia's Anastasia Pavlyuchenkova, the Serbian wining 6-3 7-6 (7/5).
France's Marion Bartoli had to come from a set down before seeing off Klara Zakopalova of the Czech Republic 3-6 6-4 6-1.
Robson, the British number two, was beaten by Kazakhstan's Yulia Putintseva 6-4 2-6 7-6 (8/6) in a match lasting close to two-and-a-half hours.
Elsewhere, Taiwan's Hsieh Su-wei swept aside American Varvara Lepchenko 6-1 6-3.