But goals from defender Wayne Thomas and substitute Michael Antonio ended Keane's hopes of a maiden managerial victory in the competition.
Even substitute Pablo Counago's last gasp strike to reduce the deficit proved no more than a consolation for the Championship strugglers.
Keane said: "The players know they have wasted a good opportunity to go further in the competition.
"I did not think we deserved to lose the game but we certainly did not do enough to win it.
"We played well in the last 15 minutes but the game starts at three o'clock and not 20 to five.
"The starting 11 was very good so nobody can accuse us of taking Southampton lightly but our performance was not up to the standard I expect."
Ipswich enjoyed the majority of possession in a first half of few clear cut opportunities for either side.
But it was Southampton, 18 league places below their visitors, who took the lead 14 minutes before half-time thanks to a wonder goal from Thomas.
There seemed little danger when Thomas picked the ball up on the right wing, but the centre-back cut inside before planting an unstoppable 25-yard piledriver into the top-left corner for his first FA Cup goal in five years.
Ipswich thought they had equalised three minutes after half time when Carlos Edwards' long throw-in deceived everybody, including Southampton goalkeeper Kelvin Davis.
But referee Andy Hall disallowed the goal after correctly spotting that none of the half dozen waiting Ipswich players got a touch on the ball before it crossed the line.
Substitute Antonio looked to have sealed victory for the 1976 winners, slotting home from two yards after Ipswich goalkeeper Arran Lee Barrett had parried Rickie Lambert's free-kick into his path.
Counago threatened to stage a late fightback when he raced clear of the Southampton defence before slotting past the on-rushing Davis in second-half stoppage time but Saints held firm to move into the fifth round.
Southampton manager Alan Pardew, who led West Ham to the 2006 final, said: "It was a hotly contested tie between two evenly matched teams and we had to dig deep.
"Ipswich have got some good young players, who get around the pitch very well and we struggled to cope with that in the first half.
"Wayne's goal was a bit of a surprise to me but he played well today and deserved his moment of glory.
"You won't see many better strikes than that in the whole competition and the second goal came at a very good time for us."
Source: Team Talk
Source: Team Talk