Bilic's forwards fluffed their lines as Andy Carroll and Enner Valencia could only manage to find the back of the net 14 times.
"Everyone knows we want a top-class striker. And if we can get a 20-goals-a-season man, there's no reason why we can't improve on last season and challenge the Premier League's top teams," Bilic told the club's website.
West Ham have already dipped into the transfer market as they looked to improve on their seventh placed finish in the Premier League, having signed defender Havard Nordtveit and winger Sofiane Feghouli on a free transfer.
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Bilic revealed the club had to ward off interest from several clubs fighting for the duo's signatures.
"We are proud and glad that he (Feghouli) and Havard Nordtveit, the captain of Borussia Moenchengladbach, have signed for us because other big clubs were trying for them," the 47-year-old said.
(Reporting by Shravanth Vijayakumar in Bengaluru)
