Wigan are now three points adrift of Aston Villa and safety, with manager Roberto Martinez targeting three wins from their remaining five matches to be safe.
"We are disappointed we couldn't get any points today because we are getting into the critical point of the season," the Spaniard said.
"We were very soft in terms of keeping that clean sheet. We know what West Ham can do and the goalscoring ability they have and I don't think we were strong enough.
"I enjoyed the second half performance. I thought that was a dominant as you would see an away team. I won't be able to explain how we lost the game.
"There is no margin of error. We have five games and we need probably three wins. That is something we can achieve.
"We were the better team today. We need to address not conceding cheap goals but in every other department we were the better team."