Keegan returned after a four-match absence following back surgery but witnessed a dire display which was enough to give him a relapse.
Saints' strike duo of James Beattie and Kevin Phillips scored all three goals to leaved City rooted close to the drop zone.
And Keegan later admitted: "We probably got what we deserved. It was not the level of performance needed to win a game.
"Southampton played without the tension and worries we have. And while it was not the result we wanted, we are not desperate because our destiny is still in our own hands."
Saints manager Paul Sturrock added that he could smell nervousness throughout the City side.
Sturrock was delighted with the way his side hit back following last weekend's defeat at Middlesbrough.
He said: "We are a decent side, but our only problem is when we think we are good players.
"But they showed with hard work, attitude and shape what we can achieve.
City were forced to reorganise their side after only 11 minutes when Steve McManaman limped off with the Achilles injury he originally picked up at Spurs five days earlier.
There was an early let-off for City when goalkeeper David James sliced a clearance following a back pass from Michael Tarnat, but Saints' David Prutton was unable to capitalise.
It was then the turn of the Saints to enjoy some luck after Robbie Fowler's brilliant throughball released Nicolas Anelka who, with only goalkeeper Antti Niemi to beat, unbelievably shot wide.
City had another great chance when substitute Trevor Sinclair's flicked near post header from Tarnat's corner beat Niemi only for Paul Telfer to save the day with a goal-line clearance.
But it was the Saints who moved into the lead in the 34th minute when Beattie scored his 16th goal of the season.
Rory Delap sent Marian Pahars away down the left and the little Latvian sent over a perfect cross for Beattie to find the net with a diving header from seven yards into the top corner.
And Telfer might have doubled Saints' lead moments later with a long-range drive which whistled just wide of the upright with James beaten.
City continued to be wasteful in front of goal with Anelka and Antoine Sibierski both heading wide when they ought to have hit the target.
And City left the field at half time to a chorus of jeers from their disgruntled fans.
City's problems intensified when the visitors doubled their lead early in the second half when Phillips netted his 11th goal of the season.
Beattie headed on Delap's long throw at the near post and Phillips rose at the far post to head in from six yards.
Keegan made two immediate changes hauling off Fowler and Paul Bosvelt replacing them with Paulo Wanchope and Claudio Reyna, but to little avail.
City were handed an unexpected lifeline with 13 minutes remaining when Wanchope broke clear on the left and rounded Niemi before cutting the ball back for Anelka to slot home his 23rd goal of the season.
The joy was short-lived as four minutes later Southampton restored their two-goal advantage when Phillips struck again with a marvellous solo effort.
The striker latched onto a long clearance out of defence inside his own half and sprinted about 60 yards to beat James with a deadly finish low to his right.
And it was a measure of the fans' disillusionment that the City of Manchester Stadium began to rapidly empty after their defeat was sealed by Phillips' goal.
MAN OF THE MATCH: Kevin Phillips - His fabulous individual goal capped a fine attacking display by the visitors.