Boss Mark Hughes has denied he is under pressure after fans called for his head as Fulham extended their winless run to eight Premier league matches.
West Ham moved level on points with the Cottagers after beating them 3-1 and Hughes conceded his men must improve.
Hughes said: "The chairman [Mohammed Al Fayed] understands what we are lacking and that we are working really hard. On occasions things have gone against us.
"We play some good stuff but it's evident we lack a cutting edge."
Hughes left the Craven Cottage pitch to chants of "Hughes out!" after earlier enduring taunts of "You don't know what you're doing!" and needs his men to pick up points at Stoke on Tuesday and Tottenham on New Year's Day to ease their relegation fears.
The Cottagers boss said that the defeat only highlighted the need to get injured strikers fit and also consider signing new recruits in the January transfer window.
"In the first half we had total control and looked very comfortable," added Hughes, who has yet to savour an away win this season.
"We had the opportunity to go 2-0 up and had we taken it I think we would have gone on to win comfortably.
"We need to look at what's out there to help us. We missed the injured Moussa Dembele and he should be back for the next game but Bobby Zamora is probably out until the middle of February. If a player becomes available we may need to go into the market."
And Hughes, while insisting his players were working hard, admitted that losing a match he had targeted taking three points from had come as a blow.
"We looked at this game as one felt we could win and from the opening exchanges we thought that would happen but football changes very quickly and we're not getting a lot of breaks," he commented.
"I'd expect to have more than two wins by this stage in the season, but we've played some good stuff today.
"We lack a cutting edge and our defending has also let us down today. We're disappointed but we'll go again at Stoke.
"There's some frustration from the fans and that's filtering through. We've got to overcome that and go and win matches. We have to be brave in possession and we have to be better on Tuesday."
Grant enjoys rare away win
While scrutiny over Hughes's future has intensified, his counterpart Avram Grant was delighted to have secured a win that moved West Ham off the bottom of the table and also lifted some of the pressure from his shoulders.
Grant reflected: "It was a good game for us - we came back, which was amazing. Fulham had a lot of possession and they were controlling it without creating chances.
"They were better than us. I didn't like the goal we conceded but we scored three and in the second half and we could have scored more so I'm happy. The players are happy with the win and they want to taste it again.
"I'm very pleased and I'm sure it won't be the last we win this season."
On Carlton Cole, who scored twice, Grant added: "He's had hard times - every player has them - [but] in the last week he's trained very hard and when you train hard and you work hard then you get the reward."
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