The Hammers, who had beaten their West London counterparts 2-1 earlier in the campaign, were the better side but failed to convert any of their chances.
The first opportunity Peter Brabrook's side created was in the 11th minute, when Danny Morris shot straight at the keeper after a good run into the area.
Morris then found strike partner Greg Pearson, whose shot was saved by the legs of Fulham goalkeeper McFrederick before Morris and Pearson combined once again only for the latter to watch as McFrederick again saved well.
Nine minutes before the interval, a scramble in the Fulham box saw the ball fall to Marcel Collington, who couldn't connect fully and the ball was cleared.
West Ham started brightly in the second half and on 47 minutes a Craig Saunders free-kick was saved well by McFrederick. Moments later the impressive Collington made a run into the area but his effort was easily gathered by the keeper.
On 59 minutes, yet another run down the right by Collington almost reaped rewards as he lost his marker and cut inside but his effort on goal was blocked by a defender.
With 20 minutes remaining, Pearson fired over the bar before George Sealey was called into action, keeping out an effort that was destined for the top corner. Collington then switched to the left wing and caused the Fulham defence problems straight away, cutting inside firing an effort just over.
In the final few minutes West Ham created a couple of chances as an Ian Tucker pass was met by Pearson, who fired over. Then two of our substitutes combined, with San Lee finding Danny Bunce, who only had the keeper to beat from six yards out but was denied again.
In the closing moments of injury time, Fulham could have snatched victory but, with only Sealey to beat, their striker fired wide.
Team: Sealey, Parrington, McClenahan, Tucker, Fletcher, Ferdinand, Collington, Saunders (Bunce 86), Morris (Lee 77), Pearson, Cole (Noble 45). Subs Unused: Reed, Blewitt.
*Under-19s report to follow soon.