In the first meeting of the two sides since a League One clash in 2011, Saints ran out victors at St Mary's with a 2-0 success - but it could have been much worse for Eddie Howe's visitors if Southampton had kept up their frenetic first-half pace.
The hosts dominated the first half, quite apt given the fact Sunday was All Saints Day after all, and deservedly led at the break as Steven Davis and man of the match Graziano Pelle - who celebrated by performing a makeshift haka with club masseur Graeme Staddon from New Zealand - scored within six minutes of one another.
But Koeman's side took their foot off the gas after the interval and allowed Bournemouth to control the tempo - although a lack of cutting edge meant the Cherries failed to test Maarten Stekelenburg until the closing minutes.
By then the chance of points for Howe's men had gone.
So, too, had Southampton's midfield general Victor Wanyama who was dismissed having picked up two yellow cards - but his absence will be felt more in next weekend's game against Sunderland rather than in the last 10 minutes here.
Koeman may have seen his side relax after the break but he insisted replicating their buccaneering first-half display was never going to happen.
"I'm not disappointed," he said when asked about the second-half.
"It is impossible to play 95 minutes in the way we played the first 45
You always get a reaction from the opponent and that makes it difficult.
"Of course we didn't not have that domination in the second half, we lost more battles and more passes and it was not the same.
"It also depends on the opponent, who put everything in the second half.
"We had a good example against Leicester and we learned from the Leicester game
Of course we like to continue playing and be more dangerous like the first half but if you play 95 minutes on the level we showed in the first half is, in my opinion, is impossible."
Southampton had already seen Pelle and Sadio Mane have shots deflected behind with the latter also firing over when well-placed before the goals came.
Bournemouth, on the back of successive 5-1 defeats in the league, were on the back foot and there for the taking as Koeman praised the opening half as the best in a long time.
"It was the best 45 minutes - maybe the best in more than one year," he added.
"With the high tempo, we had good ball possession
If you watch the two goals it is all about the high level of football and I'm very pleased about that.
"Still we have to learn from mistakes and we k now you get the reaction of the opponent after half time, that is normal and it is how you deal with that reaction
Keep winning battles, keep confidence, okay we could do it better than we could in the second half."
Howe agreed with Koeman's assessment of Southampton but thought his players had allowed their opponents to express themselves before coming back at them after the interval after a double change at half-time.
When asked about Koeman's comments on Saints' performance, the Cherries boss replied: "We contributed to that,
"They were very good and I'm not taking anything away from their performance but physically we were not where we needed to be.
"It is a difficult one for us to work out, the first half performance to the second half
The personnel changed helped, first half we weren't ourselves in or out of possession.
"You have to give Southampton credit but the pleasing thing is the players put in the performance in the second-half and the only thing missing was the goals."
The defeat means Bournemouth have now lost four of their last five league games and they sit 17th ahead of next weekend's visit of fellow strugglers Newcastle.
Source : PA