City could not pull off a second Premier League scalp in succession despite an outstanding second-half display at Southampton.
In truth, the esteemed hosts could easily have added to Gaston Ramirez’s 15th minute volley having dominated the first half, but Elliot Parish kept the Robins in contention at the interval with a string of fine saves.
Not for the first time this season, the keeper’s team-mates stepped up a gear after the break, with Jay Emmanuel-Thomas at the heart of a collection of moves from which City might easily have drawn level.
But Saints defender Jos Hooiveld headed home a corner seven minutes from time to cement his side’s place in the fourth round of the Capital One Cup.
Sean O’Driscoll made four changes to his side beaten 3-2 by Swindon Town last time out, with Stephen McLaughlin handed a first start on the left of a five-man midfield.
Joe Bryan and Bobby Reid were recalled inside of the Irishman, while Parish continued his tradition of starting cup matches in goal.
City started brightly, with Reid epitomising the early spark to their play by intercepting a loose pass from Jack Cork and flying past Hooiveld, only for the Dutchman to cynically bring him down and take an early booking for his troubles.
There was reason to feel aggrieved when Jay Emmanuel-Thomas struck the resulting free kick against the edge of the wall – a mood not helped by Ramirez’s sublime opener soon after.
When Derrick Williams slid in to repel James Ward-Prowse’s shot, the ball bounced back for the midfielder to set up his team-mate for a quite brilliant 25-yard volley not dissimilar to the one scored by Crystal Palace's Owen Garvan past Parish in round two.
The Uruguayan international – who cost £12m from Bologna last year – looked a class apart, and his clever through ball should have created the Saints’ second for Tadanari Lee, but Parish was out quickly to make a fine save with his feet.
The City keeper was expecting his busiest night of the season, and wasn’t being let down by the top flight hosts.
Ramirez unleashed another left-footed thunderbolt that whistled just past the post before Lee tested the former Cardiff City stopper again with a rising drive which needed tipping over at the near post.
At the other end, lone frontman Emmanuel-Thomas worked a shooting opportunity on to his left foot which forced Kelvin Davis into his first save, sprawling down to his left to push the ball behind for a corner.
For all Southampton’s control, City remained a threat and Emmanuel-Thomas started an excellent team move culminating in a shot from McLaughlin into the side-netting, although the offside flag would have ruled out an equaliser in any case.
Ramirez came close with another long-ranger as the home side piled on the pressure before the interval, with Calum Chambers’ mishit cross having to be tipped over and Jack Cork’s stinging shot making Parish work again.
Defender Maya Yoshida somehow headed over from point-blank range, but City weathered the storm and escaped at the break still well in the contest.
The second half looked set to continue in the same vain when Guly Do Prado threatened to double the lead with a header straight at Parish from six yards, but the Robins responded.
Emmanuel-Thomas, typically drawing defenders to the ball with every touch, created space for Bryan to guide a right-footed shot towards the bottom corner from distance which Davis was at full stretch to turn around the post.
The close shave inspired City’s best spell of the game. When Bryan was set free down the left wing, the Bristolian’s cross was just a fraction too far beyond Emmanuel-Thomas, who slid to make contact but could not divert his effort on target.
A minute later, the instrumental Emmanuel-Thomas laid the ball off for Reid to hit a curling shot which looked destined for the top corner only for Davis to touch it over the bar just as it was dipping into the net.
The visitors had the distinguished hosts rattled. Emmanuel-Thomas waltzed into the box and sent a teasing ball across the six-yard box begging for a touch from the onrushing McLaughlin, who was only inches away from turning the ball home at the back post.
Unconverted crosses were to prove a recurring theme in the latter stages as City piled on the pressure.
McLaughlin again came close when Davis failed to deal with Brendan Moloney’s centre, before Nicky Shorey sent a low ball across the box which nobody could connect with.
By now O’Driscoll had thrown on Marlon Harewood and Neil Kilkenny in search of a finishing touch, while Southampton replacements Harrison Reed and Jay Rodriguez combined at the other end on a rare counter-attack in which the latter was guilty of lifting his shot high into the sparsely populated stand behind Parish’s goal.
But Hooiveld would not make the same mistake, heading home Ward-Prowse’s late corner – just as Sam Baldock was readying himself to come on – to kill the tie and send the Saints into the last 16.