The Saints went into the break 1-0 up at Upton Park, but Koeman was keen to warn his players that West Ham would react to being behind.
And the Dutch boss was correct, as the Hammers changed the game around after bringing Andy Carroll on.
The England international’s presence caused Southampton’s defence no end of problems, and the hosts ended up winning the contest 2-1 - after goals from Michail Antonio and Carroll.
And Koeman explained: "We spoke at half-time and said that there will be a reaction [from West Ham]. They'll bring in Carroll, and they'll play the long ball, fight for second balls and be more aggressive.
"But in the first 20 minutes, we lost easy ball possession and that gave West Ham the belief to come back. That's football, and that's the reaction of the opponent.”
Southampton had gone into their match against West Ham on the back of a 4-0 victory over Arsenal.
However, their confidence looked fragile at Upton Park.
Southampton have been in poor form recently, and have won just one of their last eight Premier League matches.
Their lack of wins has seen them fall into 12th place in the standings, with the south coast side’s next fixture coming against Norwich City on Saturday.