The Croatian boss admitted there were too many "passengers" in the defeat by Swansea.
The Hammers' penultimate outing at the Boleyn Ground ended in mild embarrassment as goals from Wayne Routledge and Andre Ayew opened up a 2-0 half-time lead, before further efforts from Ki Seung-yung and Bafetimbi Gomis, either side of a Stephen Kingsley own goal, compounded a miserable afternoon.
Bilic's side had slim hopes of a top-four finish prior to the defeat, and they brought some excellent form into the contest after winning their previous two games by an aggregate score of 6-1, but their hopes of Champions League football are all but gone.
Consequently, Bilic was perfectly frank in his assessment of the performance, claiming that he simply had "too many passengers" and not enough of players taking matters into their own hands.
"I'm not that disappointed with our play with the ball, but without the ball we had too many passengers, relying on someone else to get the ball and play it to me in a good position. If you approach a game like that it makes it very difficult," he said via BBC Sport.
Sixth-placed West Ham will be leapfrogged by Southampton into the final Europa League spot if the Saints win at Spurs this afternoon, though Bilic and co can reclaim it ahead of the final game of the season by winning their game in hand in midweek - a visit of Manchester United for the last ever match at the Boleyn Ground.