Goolagong Cawley wasn't surprised that Williams was unable to back up for her fourth match in less than a week since making her grand slam comeback after the birth of her first child only last September.
The 23-time Grand Slam champion added that she would stay in Paris for scans on the injury to find out how long she will be out of action.
Williams told reporters at Roland-Garros that she was having issues with her pectoral muscles, saying it's hard to serve.
Mouratoglou said: "There's no way she can play at the moment, but I also feel that one extra match would have made it really worse and put Wimbledon in danger, but I think she stopped at exactly the right moment".
The last French woman to win a singles Grand Slam title was Marion Bartoli, when she won Wimbledon five years ago.
In Paris to receive the International Tennis Federations's highest accolade, the Philippe Chatrier Award on Tuesday night, Goolagong Cawley remains an unabashed Williams fan.
The athlete said she first noticed chest pain during a victorious match against Julia Görges on Saturday, June 2.
'I'm going to get an MRI tomorrow.
"Plus I wanted to try different tapings and different strappings and lots of different stuff to see what was helping and what I could try in my singles match. So I thought it was a flawless opportunity for me to kind of see how I would be and how I would go in that".
Garcia, whose best performance at a major came a year ago when she reached the last eight in Paris, still has to deliver, but she peaked at a career-high seventh in the WTA rankings this month.
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It means the much-anticipated clash with Sharapova has been cancelled and the Russian will now go straight through to the quarter-final.
"I think Serena can get close to winning another Grand Slam".
"I wish her a speedy recovery and hope she returns to the tour soon". "It's hard because I love playing Maria", Serena said.
"I made a promise that if I'm not at least 60 percent or 50 percent, then I probably shouldn't play", she added. "I've pretty much had every injury in the book [but not this]", she said.