The Hammers and Saints face the second legs of their third qualifying round ties on Thursday evening, against Romania’s Astra Giurgiu and Dutch side Vitesse Arnhem respectively.
While Southampton boast a comfortable three-goal advantage, the east Londoners head to the Stadionul Marin Anastasovici off the back of a 2-2 draw at Upton Park.
New boss Bilic will watch from the stands after being sent off in stoppage time against Giurgiu, where a largely inexperienced team will be looking to get a positive result as he rests key players for Sunday’s Premier League game at Arsenal.
“It is a crazy thing to think about,” Koeman said about resting players, before the manager damaged his Achilles in training.
“To throw everything away in the start of the Europa League legs. I don’t like that. I am a person who likes to win always and I hate losing. I hate to lose and that mentality needs my players as well.
“That is all a part of the job. I have to make decisions, my decision is not to lose the game but to win it. There have been many unusual things but we knew from the start that it is not an ideal pre-season because we have had qualification, starting from the bottom.
“I don’t like the excuse, I don’t see it as a problem, it is a situation and I’m trying to cope with it. We want to show respect but not to jeopardise the more important competition.”
None of the Hammers team that started the first leg has travelled to Romania and, of the players there, only Kevin Nolan, Carl Jenkinson and Manuel Lanzini are likely to feature heavily in the forthcoming league campaign.
Bilic admitted to having rethought his strategy after letting slip a two-goal lead a week ago in a Europa League campaign which came courtesy of the Fair Play League.
Southampton, by contrast, secured their place by ending seventh last term – their best-ever Premier League finish.
Koeman’s side continued where they let off against Vitesse, winning 3-0 in the first leg thanks to goals from Graziano Pelle, Dusan Tadic and Shane Long.
The Saints head to Newcastle on Sunday for their Premier League opener.