This was not what he quite had in mind.
For swathes of Saturday’s encounter between two of the Championship’s leading proponents of ‘pure’ football, City more than matched their opponents, a possession-based, easy-on-the-eye side like themselves.
Even though the final statistics showed that Southampton boasted 57 per cent possession, Hull did not overly suffer because of that. They were hurt by their own deficiencies, quite simply - and ones that are starting to become familiar, sadly.
The deepest – and final - cut arrived in the fifth minute of stoppage time. Southampton had been knocking on the door for a winner and it heightened the need for those in amber and black to retain total focus.
Instead, they switched off from a throw-in on the right. Kyle Walker-Peters, a raider on with clear and inherent dangers which weren’t attended to all afternoon, found Flynn Downes in space, too easily.
He supplied substitute Ryan Fraser, who swept the ball home in deadly fashion and Hull were broken.
As brutal at that moment was, City only had themselves to blame. Not just because of that, but their palpable failure to make the most of several promising situations and score more than one goal, for starters.
Their xG expected goals is modest; the 13th best in the Championship. Southampton are right at the top, by contrast. It told in the final analysis.
At the other end, there are concerns for Hull. They conceded the first goal of the game for the fourth successive occasion.
In his post-match musings, Rosenior rightly pointed out that much of what Hull are producing this season has been good.
They are a polished and progressive side with the ball at their feet and are blessed with some talented - and mainly young - footballers who will only get better with more miles on the Championship clock.
In the same breath, they also lack savvy at this level at times. A good side is not quite ready to take flight and Rosenior’s assertion that he needs to strike a balance between being pragmatic at the right moments and ‘playing the football what we do’ was another shrewd after-match observation.
Hull’s numbers on home soil are also in the balance and in danger of tipping over the edge.
Saturday’s defeat was a first in ten second-tier outings. They have lost just three times in 19 league matches in East Yorkshire during Rosenior’s time in charge; a pretty admirable feat.
That said, the statistics warrant closer inspection. There have been 10 draws, with four of them arriving this season. City have won just once in six Championship outings at the MKM Stadium so far in 2023-24.
Failure to beat Preston this weekend would run the significant risk of changing perceptions and pointing the finger in terms of City’s deficiencies in front of their own supporters and start to ignore what has gone before.
Operating with two wingers in Jaden Philogene and Jason Lokilo, City brought plenty to the table in the first half against high-calibre opponents.
On the debit side, they conceded a soft opener. Fortunately, they were level soon after.
It was a watchable game, but one where defences hardly covered themselves in glory.
City did at least have a bulwark of resistance in keeper Ryan Allsop. He made a fine one-handed tip-over early on after Will Smallbone’s shot took a deflection off Ruben Vinagre and looped towards goal. Allsop’s best was yet to come - so was Smallbone’s.
Philogene, who exhibited plenty of the good in his game going forward, showcased the bad in a defensive sense. His challenge to prevent Walker-Peters getting away from him was lame and the Saints’ outlet fed the unmarked Smallbone, who effortlessly guided the ball past Allsop.
Philogene’s blushes were soon spared when City levelled.
Lokilo was given too much space down the left and he slotted in Scott Twine. His ball across goal was blocked, with the rebound falling nicely for Liam Delap, who gobbled up the rebound to score for the first time on home terrain.
By the end of the game, Hampshire-born Delap - whose father Rory played for the Saints - had mixed feelings about the day.
Before his strike, he had dallied when sent clear after a slip from Taylor Harwood-Bellis. A delay for a split-second also proved telling when he had a sight of goal on the resumption. Both efforts were blocked.
Southampton's finishing was less tardy.
They forced Allsop in magnificent work to somehow get a finger tip to keep out Carlos Alcaraz's faint touch in the second period and the City custodian later beat away a drive from Smallbone.
As the clock ticked, the game got stretched. Southampton persevered and Hull clocked off.
Hull City: Allsop; Christie (Coyle 65), Jones, Greaves, Vinagre; Seri, Morton; Lokilo (Connolly 76), Twine (Tufan 65), Philogene; Delap (Allahyar 82). Unused substitutes: Ingram, McLoughlin, Docherty, Traore, Sinik.
Southampton: Bazunu; Walker-Peters, Harwood-Bellis, Bednarek, Manning; Smallbone (Charles 86), Downes, S Armstrong (Fraser 84); A Armstrong (Mara 86), Alcaraz (Adams 69), Sulemana (Edozie 69). Unused substitutes: McCarthy, Holgate, Aribo, Bree.
Referee: G Eltringham (Tyne and Wear).