Bilic has found himself under pressure after West Ham's joint-chairman Sullivan criticised their performance in the last-gasp 3-2 defeat at Bournemouth last weekend.
In an article on the club's website, Sullivan said: "I was very disappointed and frustrated with the manner of our defeat. Slaven, the players and the staff all know we have to do better."
Bilic agrees with his boss but is playing down the thinly veiled threat by the co-chairman and is looking for a response against the champions this weekend.
The manager told reporters: "It was a comment on that game, and I said also we can't be happy with the way we performed and how we conceded the three goals.
"We have to improve and we have to bounce back. I am the first that wasn't happy. The players know I was not happy about the performance.
"They were not happy in the dressing room. They were frustrated. They know we didn't do well enough in that game.
"From our point of view, now we have a game against Leicester, we have to bounce back and we are ready for that."