Robson forced Russian former world number one Maria Sharapova into a tie-break in the first set but went down 7-5, before losing the second set 6-3.
And the 18-year-old 2008 Wimbledon girl's champion can hold her head high after performing well in a two sets defeat.
Robson admitted that Sharapova was always the favourite and is now keen to switch her attention to the mixed doubles, where her and Murray will play together for the first time since the Hopman Cup in Australia last year after being given a wildcard entrance.
"It's always tough playing the number two in the world," she said.
"She won the French Open so she's obviously in great form and I had chances I didn't take so it's definitely disappointing. I've still got mixed doubles to look forward to."
"It's always fun playing with Andy. We haven't played at all together since then (Hopman Cup in 2011) so it's going to be interesting, but definitely a lot of fun."
The pair take on Czech duo Lucie Hradecka and Radek Stepanek on Wednesday.
Elsewhere, British number one Heather Watson lost her second round match with Maria Kirilenko.
Watson, whose match started later than scheduled due to rain, struggled to contain the Russian and went down 6-3, 6-2 in just under 90 minutes.
"I wasn't aggressive enough and consistent enough," she said.
"It hurts that I've lost because this is my first Olympics. I feel just disappointed, the support was amazing, I feel like I kind of let everyone down as well. I gave it my all."
Watson also admitted she was surprised not to be asked to join Murray in the mixed doubles.
"I was hoping to get in," she added.
"I thought I might have deserved a spot in the mixed because of my ranking, because of how well I've been doing, especially winning a title last week.
"I'm just upset that I didn't get picked, but there's not much I can do."
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