West Ham manager called Diego Costa's goal "very cheap" but conceded Chelsea were the better side in the Blues' 2-1 win on Monday.
Costa doubled Chelsea's lead five minutes after half-time with his 17th of the season, kneeing the ball over the line after Pedro Obiang missed Hazard's corner.
The goal ultimately proved to be the difference after Manuel Lanzini swept in Andre Ayew's pass at the death, but the game was over as a contest by then.
"I'm happy with the way we started. Then we made that mistake," Bilic said "Maybe you can do it against some teams, but not against them, with the players they have they don't miss that.
"To beat them, you need them to make mistakes, not the other way around.
"The second goal, also from our point of view, was very cheap. But they deserved to win.
"They look very serious and I can see them staying at the top with the quality they have, and with how solid they are and how concentrated they are."