The game was played out in a strong wind which swirled all around The Hive London, probably a reason why there were so few chances in the opening exchanges of the game as both sides adjusted to the conditions.
New signing Medy Elito found the back of the net with a neat curling shot, only to have been flagged offside.
Jahmal Hector-Ingram had a chance for the Irons, but his shot from close range went high and wide.
Minutes later, Andre Boucaud was on the receiving end of a heavy challenge and was brought off with Wes Fonguck taking his place.
Just after the half-hour mark, Cheye Alexander made a good run down the right, got into a shooting position but his effort was saved by Nathan Trott, a man who would begin to frustrate the Barnet attack.
In the 34th minute, West Ham were awarded a penalty when Dan Sweeney brought down Hector-Ingram. Up stepped Anthony Scully but his shot was saved well by Mark Cousins who guessed the correct way, low to his left.
New number 9 Byron Harrison had his header from Josh Walker’s cross saved by Trott on the stretch.
The Bees took their pressure up a notch after the halftime break, creating plenty of good chances.
Ephron Mason-Clark found Dave Tarpey but his first-time effort went just over Trott’s crossbar.
The two linked up again minutes later, this time Tarpey having his low effort saved.
Wesley Fonguck dribbled his way into a shooting position in the 63rd minute, but just as he was going to pull the trigger, a West Ham man put in an excellent challenge to deny him.
Trott pulled off an excellent save to deny Shaq Coulthirst a goal when his goalbound flicked header was destined for the top corner, only to be met by the glove of the West Ham ‘keeper.
At the other end, Cousins had to be alert and quick off of his line to stop Hector-Ingram in his tracks as the forward went through one-on-one.
Tarpey once again was denied by Trott before Coulthirst’s effort brought a similar result in the 82nd minute.
As the clock ticked away, Dwight Pascal had a header blocked, before the last chance of the game fell to Charlee Adams whose low drive from 25-yards out was saved once again by Trott.
Barnet – Cousins (Trialist GK, 79), Alexander (Pascal, 76), Johnson, Robson (Tutonda, 55), Adams, Harrison (Coulthirst, 45), Sparkes (Tarpey, 45), Boucaud (Fonguck, 27), Elito (Kyei, 76), Walker (Mason-Clark, 55), Sweeney.
Unused – Barham
West Ham United XI – Trott, Byram, Johnson (Greenidge, 56), Belic, Akinola (Alese, 76), Oxford, Scully, Coventry (Giddings, 78), Hector-Ingram (Jinadu, 85), Lewis, Holland (Spyrides, 76).
Attendance – 467
Referee – Wayne Cartmel