Saints continue to make a mockery of the doom merchants, with this 1-0 win moving them back up to second in the Barclays Premier League.
Sadio Mane's first-half strike proved the difference as they secured a fourth successive victory at St Mary's, although Stoke made them work for it.
It was a far cry from last weekend's 8-0 humbling of Sunderland, but manager Koeman was actually more impressed by this display.
"It was difficult because we didn't kill the game," the Dutchman said.
"We created eight good chances and you know if you don't score the second one it's difficult.
"Stoke put everything in, changed the system after an hour and with the physical strength that they have it was difficult.
"Football is strange because the first half was much better than last week
I think it was one of the best first halves of the season.
"In the second half we lost sometimes too easy our position.
"They didn't create a lot, we deserved our win but it was a difficult one, more difficult than last week and maybe more nicer to win like this than last week because the lads showed great character and great ambition again.
"We had a great support of our fans and a great win."
While the scoreline was not as sweet as last week's, it offered match-winner Mane the chance to make up for last week's disappointment.
The Senegalese summer signing thought he had scored the eighth against Sunderland, only for his first goal for Saints to be harshly stripped off him by the Premier League's dubious goals panel.
"I heard it yesterday and I explained to Mane and his reaction was okay," Koeman said.
"Maybe that was the reason he came to the bench and to say this one they will not take it away again.
"He had a great performance - he's fast, he's a good player but his defending attitude is important for the team."
Mane gave Stoke a torrid time in the first half but, like his team-mates, was unable to make the same impact after half-time.
City boss Mark Hughes was pleased by the way his side responded to a one-sided opening period, but knows that 45 minutes cost them.
"From our point of view, we're a little bit disappointed with the first half, really," he said.
"We didn't really ask enough questions of Southampton, made it a little bit too easy, showed them a little too much respect, I would suggest, which is understandable to a certain extent given their exploits last time out here.
"I think that was the case in the first half
They caused us a few problems at set plays and obviously from one of the ones we didn't deal with it dropped handily for them and they've been able to dispatch the winning goal.
"Second half, I thought we were a lot better
We made a change very early on, got Mame Diouf on, and that gave us a threat in behind and that stretched the game.
"It allowed us to control of the game and in the second half I thought we were the better side, but we never really created those clear-cut chances we need to get back on level terms."
Source : PA
Source: PA