Southampton, who had around 7,000 vociferous fans at the San Siro for their first match against an Italian team, will be left wondering how they lost this match.
Even though manager Claude Puel had made six changes from Sunday’s win over Burnley, the visitors played the more eye-catching football only for their finishing to let them down.
There was plenty to enjoy in Saints’ build-up play, including marauding 21-year-old left-back Sam McQueen, who looked like a seasoned campaigner despite making his first start for the club.
However, Jay Rodriguez, Ward-Prowse, Martina, Austin – who came on for the injured Shane Long – and Van Dijk were all guilty of not being clinical enough in front of goal.
Rodriguez thought he had scored when he headed in but the referee had blown for a foul as players jostled in the area to meet a cross.
Van Dijk and Austin had the best chances but, in the closing stages, the former sidefooted a shot too close to keeper Samir Handanovic and had a header cleared off the line, while Austin’s close range effort was brilliantly blocked by the Inter stopper.
Struggling Inter perform smash-and-grab
Inter Milan might be one of Italian football’s biggest clubs but they have fallen on hard times and, even though this was not pretty, they badly needed these three points.
They were weakened by not being able to include summer signings Gabriel Barbosa, Joao Mario, Geoffrey Kondogbia and Stevan Jovetic in their Europa League squad this season because of Financial Fair Play regulations.
And the home side, who are struggling in 11th in Serie A, played more like the away team as they soaked up the pressure and tried to catch Southampton on the break.
They rarely threatened but, when they did, Candreva showed the ruthlessness Southampton lacked when he found the top corner with a left-foot strike from Davide Santon’s low cross.
It was Inter’s first win of this season’s Europa League following defeats to Sparta Prague and Hapoel Beer Sheva but they remain bottom of Group K, with Southampton second.
Man of the match – Samir Handanovic
What they said:
Southampton manager Claude Puel speaking to BT Sport: “It is very hard to lose this game because we had control of the game every time.
“I think we are unlucky because we played a very good game with quality and had many, many, chances and it is a big disappointment tonight.
Southampton captain Virgil van Dijk: “It is very tough. We were the team that deserved it most. You can see the goal was their only chance and it is frustrating, we should have buried the game in the first half.
“There was only one team who deserved to win but in the end that is football.”
The stats you need to know
Inter Milan have won their past four European games at the San Siro against English opposition, netting 11 goals.
Including qualifiers, the Saints have only recorded one victory in their past eight European away trips (D3 L4).
Southampton had 11 shots in the second half – not since September 2015 against West Brom have they had as many shots in a second half without scoring.
The Saints conceded their first goal from open play in 10 games in all competitions.
Southampton will try to extend Manchester City’s run of games without a win to five when they visit Etihad Stadium on Sunday for a 13:30 BST kick-off. Inter Milan are at Atalanta on the same day at 14:00 BST. Inter visit St Mary’s in both sides’ next Europa League outing on 3 November.
Match ends, Inter Milan 1, Southampton 0.
Second Half ends, Inter Milan 1, Southampton 0.
Attempt missed. James Ward-Prowse (Southampton) right footed shot from outside the box is close, but misses to the right.
Offside, Southampton. Steven Davis tries a through ball, but Virgil van Dijk is caught offside.
Corner, Southampton. Conceded by Gary Medel.
Substitution, Inter Milan. Danilo D’Ambrosio replaces Yuto Nagatomo.
Offside, Southampton. Pierre-Emile Højbjerg tries a through ball, but Charlie Austin is caught offside.
Attempt saved. Charlie Austin (Southampton) right footed shot from very close range is saved in the centre of the goal.
Corner, Southampton. Conceded by Yuto Nagatomo.
Attempt blocked. Virgil van Dijk (Southampton) header from the centre of the box is blocked. Assisted by James Ward-Prowse with a cross.
Corner, Southampton. Conceded by Ivan Perisic.
Attempt blocked. Oriol Romeu (Southampton) right footed shot from outside the box is blocked. Assisted by Virgil van Dijk.
Substitution, Inter Milan. Ivan Perisic replaces Éder.
Pierre-Emile Højbjerg (Southampton) is shown the yellow card for a bad foul.
Foul by Pierre-Emile Højbjerg (Southampton).
Éder (Inter Milan) wins a free kick in the defensive half.
Gary Medel (Inter Milan) is shown the yellow card.
Foul by Pierre-Emile Højbjerg (Southampton).
Éder (Inter Milan) wins a free kick on the right wing.
Attempt blocked. Pierre-Emile Højbjerg (Southampton) right footed shot from outside the box is blocked.
Corner, Southampton. Conceded by Mauro Icardi.
Attempt blocked. Maya Yoshida (Southampton) header from the centre of the box is blocked.
Attempt saved. Virgil van Dijk (Southampton) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by James Ward-Prowse.
Substitution, Inter Milan. Cristian Ansaldi replaces Antonio Candreva.
Pierre-Emile Højbjerg (Southampton) wins a free kick on the right wing.
Foul by Éder (Inter Milan).
Corner, Southampton. Conceded by Jeison Murillo.
Substitution, Southampton. Steven Davis replaces Jay Rodriguez.
Second yellow card to Marcelo Brozovic (Inter Milan) for a bad foul.
Pierre-Emile Højbjerg (Southampton) wins a free kick in the attacking half.
Foul by Marcelo Brozovic (Inter Milan).
Charlie Austin (Southampton) wins a free kick in the defensive half.