The defeat was their fourth straight and fifth from six Premier League matches. Boos greeted the final whistle.
"There is no question that this has not been the start to the season that we were looking for but rest assured we are doing everything we can to fix the situation," the chairmen said in a letter to fans on the club's website (www.whufc.com).
"The facts are there for everyone to see. We know we are letting in too many goals and not scoring enough, but be assured we will sort the problems out."
West Ham finished seventh in the league last season and secured a Europa League place.
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Record signing Andre Ayew faces a long spell on the sidelines after injuring his thigh in August, while left back Arthur Masuaku is expected to be out for at least six weeks due to ligament damage.
However, injured striker Andy Carroll is set to return to action next month.
"There have been factors which have contributed to the poor start with injuries to key players and some key decisions which have gone against us," the co-owners added.
"But we are not going to make excuses and know that Slaven (Bilic) and his team will be working even harder on the training ground this week to get things right. We will turn our season around."
West Ham next host promoted Middlesbrough on Saturday.
($1 = 0.7692 pounds)
(Reporting by Ian Rodricks in Bengaluru, Editing by Nick Mulvenney)
