The 122nd-ranked Zhang, 26, failed in her 14th attempt to win a Grand Slam match as she was beaten by 12th seed Karolina Pliskova.
"I can only be myself," she said afterwards. "It is impossible to become a new Li Na, that's why she is great."
Zheng Saisai is expected to become China's number one player late this year because of Peng's absence. The 21-year-old has showed her potential by reaching the semifinals of the Shenzhen Open in south China this year. But she is not optimistic about her chance in the near future.
"What's the point of becoming China's number one without success on the tour?" she said.
Li Na, Peng Shuai and Zheng Jie, who will play doubles at this year's Roland Garros, have helped to put China on the world tennis map. However, the dynasty they built is looking sure to come to an end when the 32-year-old Zheng, former semifinalist at Australian Open and Wimbledon, retires this summer.
And you can only wait for a new talent like Li, Peng or Zheng to come and no one knows how long it will take.