Radwanska had won the title 12 months ago, however the world No 5 was upset by American qualifier Bethanie Mattek-Sands.
The top seed was troubled by a shoulder problem during the 7-5 6-2 loss, however 24-year-old Pole insists that the defeat will not hamper her ahead of the Australian Open.
“She was really playing aggressive,” Radwanska said.
“Didn’t matter if it was my first serve, second serve, or anything, she was really going 100 percent for every ball.
“I really had a lot of good matches last week. It’s not like I’m playing bad. I’m not worried about that. I just think not my day (and)… sometimes you have to lose.
“I think every week is different story. You start over and over again.
“Every tournament isn’t the same thing. You’re not winning every week every match. Normally you just to have to start again, not really think what was happening in the last week.”
Sixth seed Caroline Wozniacki also bowed out prematurely as she lost 6-4 7-6 (9-7) to Lucie Safarova.
Second seed Petra Kvitova had no such problem in reaching the third round, though, as she blew away Christina Mchale 6-1 6-0, while fifth seed Angelique Kerber saw off Kaia Kanepi 6-3 6-4.
Carla Suarez Navarro was a 7-6 (7-4) 6-3 winner over Ekaterina Makarova, while Madison Keys was forced to dig deep during her 6-0 3-6 7-6 (7-3) victory against Ajla Tomljanovic.