Slaven Bilic's side lost 3-0 on Sunday to Southampton and have one league win after finishing seventh last season.
"We know we are letting in too many goals and not scoring enough," said the co-chairmen in a letter to the fans.
"But be assured we will sort the problems out."
West Ham have lost their last four Premier League games, conceding 14 goals, and lie 18th in the table.
Record signing Andre Ayew was ruled out for four months with injury in August, having joined for £20.5m in the summer.
"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," added Gold and Sullivan.
"But we are not going to make excuses and know that Slaven and his team will be working even harder on the training ground this week to get things right."
West Ham's joint-chairmen David Gold and David Sullivan say injuries and key decisions have gone against them this season but they are doing "everything they can to fix the situation".