The Hammers have brought in seven new faces this summer and more look set to follow.
“There’s not a lot to say unfortunately, I can only repeat what I said a few days ago. We are trying to sign one or two players, not five,” said Bilic, in quotes published on the club's official site.
West Ham have brought Angelo Ogbonna, Pedro Obiang and Dimitri Payet for substantial fees this summer, and Bilic spoke of the difficulties of operating within a strict budget.
“It is hard, it’s not easy, it can be frustrating when you see other club’s that have absolutely no limit whatsoever budget wise, even they are struggling, especially to find strikers.”
"But we are confident we will get one, and even if we don’t we have a good team. Of course we will have to be lucky with injuries, that’s normal.”
West Ham got off to the best possible start at the Emirates on Sunday and clearly have the nucleus of a competitive squad.
Additions are still needed in a couple of key areas however, with central midfield and up front the most pressing concern.
The failure to secure the signing of Alex Song has left something of a void in the Hammers midfield and there is no guarantee that midfield enforcer Pedro Obiang will adapt to the demands of the Premier League right away.
Reece Oxford’s emergence has been an added boost but relying on the 16-year old to perform consistently over a long campaign would also be unwise.
In attack meanwhile, Enner Valencia’s long-term injury has been a huge blow, while Andy Carroll is a persistent fitness doubt and some added support for the likes Mauro Zarate and Diafra Sakho would be more than welcome.