First half goals from Sekou Mara and Moussa Djenepo proved to be the difference as the Premier League strugglers outclassed City.
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It is the first time in Pep Guardiola's managerial career that he has lost in a domestic cup quarter-final.
But his side didn't deserve to progress into the last four where they were second best down on the south coast having failed to register a shot on target.
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The hosts took a deserved lead in the 23rd minute through French forward Mara, who expertly tucked away his first goal for the Saints.
Mara - signed from Bordeaux last summer - fired low into the bottom right corner from the centre of the box.
The 20-year-old peeled away from Kyle Walker where he was picked out by Lyanco, with City goalkeeper Stefan Ortega given no chance.
But there were question marks over his role in Southampton's second after he was lobbed from 30 yards out by Djenepo five minutes after Mara's strike.
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Ortega was well off his line, with Djenepo taking full advantage after dipping an effort over him into the back of the net.
Speaking on talkSPORT commentary, Stuart Pearce remarked: "He's got it out his feet, and he's got so much loft on it, you thought it was going way over the goal.
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"The goalkeeper's position was misleading slightly. City now have a real fight to stay in this game."
Chris Iwelumo meanwhile said on talkSPORT 2: "As a goalkeeper you can't expect to be on your penalty spot when a player has the ball 30 yards from goal.
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"That's a really poor starting position, but take nothing away from Djenepo."
Guardiola turned to his bench in the second half, with Erling Haaland, Kevin De Bruyne, Rodri, Nathan Ake and Manuel Akanji all coming on.
But it proved to be ineffective as City were still reduced to scraps, as they failed to trouble Gavin Bazunu.
Southampton had lost their last six Premier League games going into the match, though they were buoyed by the recent FA Cup third round win away at Crystal Palace.
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For Guardiola, Wednesday night's result will be the worst possible preparation ahead of Saturday's derby clash against Manchester United.