Algerian winger Sofiane Feghouli, Senegalese pair Cheikhou Kouyate and Diafra Sakho and Ghana international Andre Ayew are all expected to join up with their respective countries for the three-week tournament in Gabon which begins on Jan. 14.
West Ham have endured a turbulent campaign after finishing seventh last season and are four points above the relegation zone.
"It's not ideal that three or four of our players will be heading to the African Cup of Nations. But it's at the same time as the transfer window," Bilic told a news conference on Friday.
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The Hammers got temporary relief with Wednesday's 1-0 win over Burnley, a first victory in seven games, and face another struggling side on Saturday in Hull City, second bottom of the table and with just one win in their last 14.
Even though West Ham picked up the three points against Burnley, Bilic accused his side of suffering from a lack of confidence after taking the lead in the first half.
"In the second half I saw what I call that cramp, when you are afraid of winning," said Bilic who has a full squad available for the game.
"It happens to clubs who are under-achieving. I don't want it. The only way it goes away is by winning games and climbing the table. Hopefully, on Saturday against Hull we will see less of that cramp, and we will be more confident."
(Reporting by Richard Martin, editing by Ed Osmond)
