Coventry 1-2 Southampton
Aaron Martin added to Coventry's misery with a late winner as Southampton made the fourth round of the FA Cup.
Gary McSheffrey's 12-yard half-volley had given the Sky Blues an early lead before 17-year-old James Ward-Prowse levelled from Danny Fox's cross.
But Saints sealed victory in the all-Championship tie thanks to the first senior goal of Martin's career.
Coventry have now lost six of their last eight games, and home fans protested before and during the game.
McSheffrey's fifth-minute opener was missed by around 200 or more protesting Coventry supporters who had gathered outside the ground.
The hosts, who wore a 1987-inspired replica kit to mark the 25th anniversary of their famous Wembley win over Tottenham, broke the deadlock when Cyrus Christie's cross allowed Gael Bigirimana to set up McSheffrey from 12 yards.
City keeper Chris Dunn denied Ward-Prowse early in the second half but the lively youngster made no mistake from close range in the 64th-minute after converting a cross from former Coventry full-back Fox.
Coventry's misery was complete when Martin met Fox's outswinging corner with eight minutes left and his header squirmed over the line.
Coventry manager Andy Thorn:
"We need men, we don't need shrinking violets. We were not as manly as we could have been.
"Both were soft goals to concede. My son, Jack, is ten years old and he could have scored both of them.
"You have to have the desire to want to win the ball in our box which we didn't on both goals. You can't accept things like that. If I was a player in the dressing room, I wouldn't if my team-mates were prepared to do that.
"We have to concentrate for 90 minutes, we can't switch off otherwise all the hard work we have put in goes to waste. That is what's most frustrating.
"It isn't like we don't work on it because we do all the time. We have to learn fast."
Southampton boss Nigel Adkins:
"We have a crop of youngsters we believe in and we need to aid their development path through to get experiences - good and bad - so that they can keep developing.
"Great credit must go to all the staff in our academy and first team because we want to get to a stage where 50% of the youngsters go through into the first team but that takes time. The future is bright.
"We had had two poor results - the performances were not too bad - but results went against us. Today was a big game for us. Great credit to all the players because they have shown character.
"The first half wasn't the greatest from our point of view but we passed the ball well in the second half to grind out a result."