Denmark's Wozniacki struggled to find any momentum as she was comfortably knocked out 6-2 6-2 by Begu.
"You always want to go onto the court and do your best no matter what's happening out there," Wozniacki told reporters. "I tried but I didn't succeed in playing well.
"I made too many errors. I definitely felt I couldn't hit through her today like I wanted to. When she had the opportunity she went in and finished off the point.
"I tried to win out there and I tried my best. It just wasn't enough today."
The 22-year-old has yet to win a Grand Slam since she turned professional.