Saints' impressive start to the campaign made a mockery of those predicting a season of woe in the wake of the unparalleled summer talent drain from St Mary's
However, Saints' best-ever top-flight start has gone off kilter in recent weeks and they enter Saturday's match against Everton looking to end a run of five successive defeats in all competitions.
It makes Roberto Martinez wary of a backlash from Saints, with the Toffees manager judging them on this season's displays rather than their recent defeats - a wise assessment in Koeman's view.
"Always you have to look until now," the Saints boss said.
"If somebody said to me in the pre-season 'after the middle of December you are the fifth in the list' I would have said 'give me the paper and I will sign it now'.
"I understand the defeats because that's always the difference with players
They need confidence and sometimes now you see that.
"I know my players, how they can play football, and it's difficult because of maybe freshness, maybe about more changes in the team.
"Confidence you can show them, you can tell them, The answer in always on the pitch Saturday at three o'clock and then you have to show it.
"There are always ways to lose a game but not how we lost last Tuesday."
That defeat to Sheffield United was comfortably the worst of Koeman's reign, given the manner in which they bombed out of the Capital One Cup to League One opposition.
"I was very disappointed but it all is the past and sometimes that's the nicest part in football," the Dutchman said about the 1-0 loss
"You get always the next game and can change a lot of things.
"Looking back to last Tuesday, we have to change our teamwork, our belief, our spirit and that's the key in my opinion for the Saturday game."
Koeman will also have to make changes himself as injury and suspension has decimated the Saints squad.
Morgan Schneiderlin, Victor Wanyama and Florin Gardos are all banned for the visit of Everton, while long-term absentees Jay Rodriguez, Jack Cork and Sam Gallagher are joined on the sidelines by Jake Hesketh and Dusan Tadic.
Furthermore, Steven Davis and Graziano Pelle are doubts for a match which Koeman will have to blood in some of Southampton's young talents.
Everton goalkeeper Tim Howard insists Ross Barkley has no problem handling expectations as his team-mates are always on hand to bring him back down to earth.
The 21-year-old midfielder enhanced his reputation further with a brilliant opening goal in Monday's 3-1 win over QPR.
He has regularly been likened to Paul Gascoigne and touted as the most gifted footballer of his generation.
Howard believes he has more in common with former Everton prodigy Wayne Rooney, now Barkley's international captain, and Liverpool's Steven Gerrard.
The Toffees goalkeeper is confident the youngster can handle the pressure of such comparisons but admits the Everton dressing room ensures he remains grounded.
"He is special
He has a lot to learn but the thing I love about Ross - which I have not seen in a ton of other players, and I think that is why he gets named with some of the best - is he is fearless," said the United States international.
"In this country Wayne Rooney and Steven Gerrard, those guys were 'throwing fire' in their teens and early 20s, and they flourished and that is why Ross is special.
"He wants the big moments, he wants the ball and he doesn't shy away from it - when I was his age I wanted nothing to do with being near the pitch or the spotlight because it was too daunting but he is special in that regard.
"I think Ross can handle it
He enjoys that pressure, he is not afraid of it.
"His football education has been here and it continues to be here and he has guys around him.
"As special as he is, we don't let him drift off with his head in the cloud
We keep him grounded."
Gareth Barry returns from suspension but fellow midfielders Darron Gibson (knee) and James McCarthy (hamstring) are both rated 50-50 to be fit for the trip to Southampton.
Forward Kevin Mirallas will be missing after sustaining ankle ligament damage on Monday while Leon Osman (ankle) is unlikely to return this weekend.
Source : PA