The Saints, who had beaten Millwall away in the Capital One Cup earlier in the week, produced a slick display to come from behind and run out 3-1 victors at Upton Park with a brace from French midfielder Morgan Schneiderlin.
It could have been easy for Koeman's side - much changed from the one sent out by Mauricio Pochettino last season following a string of summer departures - to abandon their pass-and-move approach when falling behind to Mark Noble's deflected 25-yard effort and go more direct in search of a way back into the match.
Dutchman Koeman, though, feels Southampton are starting to see the rewards for such a positive mindset.
Schneiderlin equalised on the stroke of half-time when converting a free-kick at the back post before putting the visitors into the lead just after the hour, again from close range following a set-piece, and £8million forward Graziano Pelle secured the points with eight minutes left - which saw hundreds of disgruntled West Ham fans head for an early exit.
"We train very differently from last season - less physical exercise and more football, more positioning exercises and we showed that in the last 15 minutes at West Ham
That is the way I like to play," said Koeman, the former Feyenoord coach.
"I know we have to run and fight, but winning games is about trying to do that in a football way and we have the players for that.
"It was very important to win before the international break because now we have four points and we needed that.
"We hope that they will all come back in a good physical shape to continue what we have done up until now."
Schneiderlin has started all three league games so far, with Southampton insisting the midfielder is not for sale, having been strongly linked with a switch to join Pochettino at Tottenham.
On Saturday evening, the midfielder gave an interview with Saints' internal media channel insisting he wanted to focus on his game, but stopped short of committing his future to the club ahead of the September 1 deadline.
While the Saints will now head into the international break in positive mood, West Ham are left with a fortnight to digest what was an abject display.
Irons boss Sam Allardyce - again the focal point of fans' frustrations as he was in the midweek cup penalty shoot-out defeat to Sheffield United - hopes the defeat will serve as a "wake-up call" for the players in the challenges ahead.
West Ham announced the loan signing of Cameroon international Alex Song from Barcelona before kick-off, and Allardyce hopes the former Arsenal midfield enforcer can help move his team forwards
"It should make us better, so I hope he can get straight in there and inspire us to play more like we did against Crystal Palace and Tottenham and less like we did against Southampton," Allardyce said.
"Song is a massively talented player, but the others have to play their best to play with him and he will definitely add something to us."
Source : PA
Source: PA