United have found the net just 19 times in 14 home league matches this season and have scored only once in their last three outings.
They will again be without Wayne Rooney through injury when they host the Hammers in Sunday's FA Cup quarter-final.
And Bilic believes the lack of a world-class forward has been a major factor in their disappointing campaign under Louis van Gaal.
"Under Sir Alex Ferguson, if you see the names that played up front for them, they were either at a better age or were bigger names or better goalscorers," said Bilic.
"Now Van Gaal has some really young, talented players who are definitely going to be that, but simply they are not that consistent because of their age, and because of the situation it is very hard to be confident if you are a Manchester United player.
"But to be fair, they don't have a Sergio Aguero or a Ruud van Nistelrooy or Cristiano Ronaldo, and Rooney is injured."
West Ham head to Manchester in sparkling form having won their last three league matches against Sunderland, Tottenham and Everton.
United, by contrast, go into the match on the back of a woeful performance at Liverpool, where they crashed 2-0 in their Europa League first-leg clash.
With the likes of Dimitri Payet, Manuel Lanzini and Andy Carroll fit again following recent injury lay-offs, Bilic is confident they can take full advantage of United's unconvincing form
"If you are asking me if we are confident, we are confident because we are playing good, we are training good
We are buzzing," he added.
"If there is time to train, we are training hard
That is the biggest secret
We have good players who are hungry, who are motivated.
"Now we have the players back from injuries, we have 18 players that you can easily treat as regulars."
Bilic can also welcome back defender Joey O'Brien and wingers Victor Moses and Enner Valencia from injury for the Old Trafford clash.
Source : PA
Source: PA