"I think the audience was really tough today".
"I just think that they were a little bit, sometimes should be a little bit more respectful, even though for the game, because we had to, you know, stop".
Meanwhile, Williams won the first set against Bacsinszky before being outplayed in the final two of the two-hour, 12-minute match.
Former world No. 1 Venus Williams, the seven-time Grand Slam singles victor, fell down to Timea Bacsinszky 5-7, 6-2, 6-1, and the 2011 US Open champion Samantha Stosur was defeated by Jelena Ostapenko of Latvia at 2-6, 6-2, 6-4.
Muguruza took only 15 points in the first set as the Frenchwoman cruised to a 6-1 lead.
Caroline Wozniacki, with two slam finals now the most experienced player left, continued her fine year with a surprise 6-1 4-6 6-2 victory over 2009 victor Svetlana Kuznetsova.
Mladenovic, who is into her second career grand slam quarter-final, said she also found it tough playing in front of her home crowd.
"You know what? I love this tournament, no matter what happens", she said.
Because of showers and heavy wind much of the afternoon, the two men's singles matches on Tuesday's schedule have been moved to Wednesday: No. 4 Nadal vs. The fourth-seeded Spaniard next meets either No. 5 Milos Raonic of Canada or Spaniard Pablo Carreno Busta.
The only player to have beaten Nadal on clay this season is Austrian Dominic Thiem - who was playing Argentine Horacio Zeballos later Sunday in a fourth-round match.
"I don't think that they crossed the line", she said.
How right those folks were.
Spanish tennis star Garbiñe Muguruza had to leave a post-match press conference in tears after a French Open defeat in which the crowd was slammed as "pathetic". Obviously they are excited.
"It's still there. I mean, it's obvious that I have some struggles still, especially with my serve", said Mladenovic. "If you had been in my shoes on the court, I think you would have understood". A new Grand Slam victor is set to emerge at the tournament as none of the women's players remaining made that.
24-year-old Mladenovic was clearly excited following her win over the reigning champion and thanked the crowd at Roland Garros for cheering her on to glory.
Mladenovic pulled off the victory despite 16 double-faults, seven in each of the last two sets at Court Suzanne-Lenglen.
"I'm not ideal, I make mistakes".
Venus Williams' 20th attempt to win the French Open ended just like the other 19 - with her not the last person standing in Paris.