"The strikers didn't score enough goals or as many as we expected but it is not only down to them," Bilic told British media.
"I never want to divide the team into strikers and the rest. Although it is the strikers' job to score goals, it is also the responsibility of the whole team."
West Ham have been linked with a move for Sturridge in the January transfer window, and Bilic said he admired the England international's natural ability.
"He's one of the biggest talents, he's a great player," the manager said.
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"The talent is there, the touch, the finishing, everything is great. The only thing that's stopped him being regular for club and country are the injuries."
Sturridge, who has lost his starting place to Brazilian Roberto Firmino under manager Juergen Klopp, will sit out Sunday's match with a calf injury, and Bilic would not confirm if he would bid for the striker in January.
"He's just a player that has been linked with us, basically, and we've been linked with almost every player," he said.
"We're always there in contention. Most of the time it's absolutely not true, 95 percent of the time. But you're asking me about Sturridge and I have no problem about that.
"All the clubs are thinking about him because he is that kind of player. I don't know his work rate, I don't know his dedication to his job or whatever but unfortunately for England and for Liverpool and especially for him he's injured. That's his problem."
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
