Wozniacki, who has failed to reach the quarter-finals in any of the Grand Slams this year, concedes that it has been a disappointing 2013 for her.
"I had many break-point opportunities in the second I didn't take and all of a sudden she came into the rhythm and just started hitting everything and it was starting to go in," Wozniacki told reporters.
"She put me under pressure and I started to play a little short, and then all of a sudden she was all over the ball. She took very high-risk shots and things were going in for her. I was really trying to fight for every point and fight as much as I could, and it just wasn't enough today.
"It wasn't the best year for me at the majors but there is next year. Overall I feel the progress has been good. I have been hitting the ball well and playing well. I hope there will be more positives in the end of the season."
Meanwhile, Giorgi plays 10th seed and compatriot Roberta Vinci in the next round.