Williams, who suffered her earliest Grand Slam exit since Wimbledon 2014, was given a standing ovation as she walked off Court Philippe Chatrier while sections of the crowd jeered her conqueror.
The 37-year-old eased past Argentina's Leonardo Mayer and will face either close friend Stan Wawrinka or Greek sixth seed Stefanos Tsitsipas for a semi-final spot.
The Italians travel to Athens to take on Greece on June 8 and before hosting Bosnia in Turin three days later, and Mancini said the 28-year-old could only blame himself for not being selected.
Among them was Kemam Kalkavar, a Turkish engineer and lifelong Liverpool fan who flew from Ankara with a group of friends for the match and was willing to pay €5,000 ($5,575) for a ticket.
Maurizio Sarri held talks with Chelsea director Marina Granovskaia on Friday and informed her that he wanted to return to his homeland, the reports in Britain and Italy said.
The torch will also visit the Hiroshima Peace Memorial Park and pass Mount Fuji before arriving at the National Stadium in Tokyo on 24 July during the Olympics opening ceremony.
Reyes, who shot to fame at Sevilla before a switch to Arsenal followed by spells at Real and Atletico Madrid, was on the books with second tier Spanish club Extremadura.