Ferdinand was culpable for Edin Džeko's second in City's 3-0 rout and has admitted the champions' decline has left him feeling uncomfortable.
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Ferdinand started in the 3-0 defeat to City on Tuesday night
"It's embarrassing - it becomes a personal insult," Ferdinand said on BT Sport. "I don't want to go out when the game is finished and you even stop watching TV. I don't want to take my kids to school.
"I don't want to walk on the school path and think I'm hearing things or seeing people look at me because we lost a game.
"I don't want to fill my car up with petrol or go to the shops. It gets personal with everyone looking at you and talking about the results and the form and stuff.
Rio Ferdinand's United career
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The John Travolta revival went down surprisingly well with Sir Alex Ferguson
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Debut, vs Zalagerszeg in August 2002
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Title no.1 in 2003
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A regretful Ferdinand looks on after the FA announced he would be banned eight months for missing a drugs test
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Limping out for 2/3 of the year at Wolves in January 2004
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Coming back against Liverpool in September 2005 (credit:Getty Images)
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Ferdinand was named man of the match after a terrific display (credit:Getty Images)
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Goal no.1 vs Wigan
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Goal no.2 vs West Brom
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Liverpool, a team Ferdinand scored against with Leeds, are on the receiving end of a 90th-minute winner in January 2006
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With Nemanja Vidić, Ferdinand has forged one of United's greatest defensive partnerships
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Liverpool get 'merk'd' again in October 2006
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Title no.2, 2007
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A first - and only - Champions League goal for United in Kiev, October 2007
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Enjoying a fortuitous goal at Villa Park later that month
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Ferdinand savours his volley against Newcastle in January 2008
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Title no.3, 2008
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European champion
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World champion (credit:Getty Images)
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League Cup winner for a second time in 2009
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Title no.4
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Title no.5, 2011
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Still going strong
FBL-ENG-PR-MAN UTD-SWANSEA(24 of26)
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Manchester United's English defender Rio Ferdinand (R) celebrates scoring his team's second and winning goal during the English Premier League football match between Manchester United and Swansea City at Old Trafford in Manchester, northwest England, on May 12, 2013. AFP PHOTO / ANDREW YATES RESTRICTED TO EDITORIAL USE. No use with unauthorized audio, video, data, fixture lists, club/league logos or “live” services. Online in-match use limited to 45 images, no video emulation. No use in betting, games or single club/league/player publications (Photo credit should read ANDREW YATES/AFP/Getty Images) (credit:Getty Images)
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Manchester United's English defender Rio Ferdinand lifts the Premier League trophy after the English Premier League football match between Manchester United and Swansea City at Old Trafford in Manchester, northwest England, on May 12, 2013. AFP PHOTO / ANDREW YATES RESTRICTED TO EDITORIAL USE. No use with unauthorized audio, video, data, fixture lists, club/league logos or “live” services. Online in-match use limited to 45 images, no video emulation. No use in betting, games or single club/league/player publications (Photo credit should read ANDREW YATES/AFP/Getty Images) (credit:Getty Images)
Manchester United Premier League Winners Parade(26 of26)
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MANCHESTER, ENGLAND - MAY 13: Rio Ferdinand of Manchester United uses the microphone to get the crowd singing at the start of the Premier League trophy winners parade on May 13, 2013 in Manchester, England. (Photo by Christopher Furlong/Getty Images) (credit:Getty Images)
"You don't want to live like that. You want to live freely and comfortably."
Ferdinand will leave United in the summer after 12 triumphant years at Old Trafford, where he has won six championships, two League Cups, the Champions League and the Club World Cup.
After a resurgent 2012-13, Ferdinand signed a one-year extension but has played just 19 times under David Moyes this term and his form has nosedived.