Roma were leading 3-0 at Genoa before collapsing in the second half to lose 4-3, prompting the club hierarchy to declare that they were to consider Ranieri's future on Monday.
Claudio, however, has pre-empted their meeting by resigning on Sunday evening.
The ANSA agency reported Ranieri as saying, "I always tried to think in the best interests of the team.
"After a match like today's, I think it's the fair thing to do to send a sign.
"When the final whistle sounded, I went into the locker room to thank the team, and I decided to resign.
"I hope that this decision helps to encourage the squad."
So Near Yet So Far
Roma's 2011 capitulation signals an ignominious end to an Olimpico career that once seemed promising.
Ranieri took the reins of the Lupi in 2009, succeeding Luciano Spalletti. His first season in charge very nearly saw Roma recapture the Scudetto, which they last won in 2001, only to lose out to Inter by two points.
The 2010-11 season, though, was one of almost total disappointment. As of Ranieri's final game Roma were 8th in Serie A, leaving them almost completely out of the runnings for a Champions League place.
Claudio Ranieri's Roma Record
Won: 32 (57.1%)
Drawn: 13 (23.2%)
Lost: 11 (19.7%)
Once in the last 16 the Giallorossi lost out at home to Shakhtar Donetsk at home in the first leg.
Roma are yet to have yet to issue an official statement of their own regarding Ranieri's resignation, meaning that there is also no confirmed word on who is set to replace the coach, even temporarily.
However, sources in the Italian media indicate that Vincenzo Montella could be in line to take over. The 36-year-old spent a decade with the Lupi, scoring well over 100 competitive goals during his time in the Eternal City.
It is expected that club president Rosella Sensi will release a statement on Monday.