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.