Following a 2-1 defeat to Liverpool and a goalless home draw with West Brom, Southampton travel to Upton Park on Saturday still searching for their opening league win of the new season under the Dutchman, who took over from Mauricio Pochettino in June.
Southampton did record a 2-0 League Cup second-round success at Millwall on Tuesday, and Koeman is now eager to build on that triumph.
However, the 51-year-old knows that will be no easy feat at a ground where the south-coast club were beaten 3-1 last season and 4-1 in 2012-13.
"It's always important [to win] because that's the best way to have the confidence. You can talk, you can believe but points always bring in a good feeling," Koeman said.
"We had a good match against Liverpool, we lost. It wasn't a good one against West Brom but we have to be prepared because West Ham have started in a good way this season and it's a tough team to beat.
"It's an aggressive team - they play in an aggressive, physical way and I think it's a little bit different than our philosophy, but it's always difficult to beat that kind of team."
There are no new injury worries for Southampton, with Lloyd Isgrove, Sam Gallagher and Jay Rodriguez all still on the sidelines due to knee injuries.
Striker Diafra Sakho is a doubt for West Ham after suffering a back problem.
News of the Senegal forward's injury will come as a blow to the hosts, as captain Kevin Nolan (shoulder) and striker Andy Carroll (ankle) are in the treatment room, in addition to Carl Jenkinson, James Collins (both hamstring) and Matt Jarvis (thigh).
West Ham produced an impressive performance to win 3-1 at London rivals Crystal Palace last Saturday, seven days after failing to break down Tottenham in a 1-0 defeat on the opening weekend.
And, with the talismanic duo of Nolan and Carroll out of action, manager Sam Allardyce has called for his side to be more clinical in the final third of the pitch.
"With a new manager, Southampton will have players who want to impress him," Allardyce said.
"Having watched the Liverpool game, they put up a good performance and then got a draw at home.
"We need a little more consistency in front of goal and we'll be fine."
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