The Hammers offered little going forward and were unable to live with their opponents at times, as the hosts picked up their biggest Premier League victory under Jose Mourinho.
Bilic admits that the opening match could not have gone much worse for West Ham, but has urged his charges to quickly pick themselves up ahead of next week's meeting with Southampton at the London Stadium.
"We have to admit they were better than us in every department," he told Sky Sports News. "[They were] better on the ball, off the ball and in 50-50 challenges. If you make the mistakes like we did from promising situations, add to that a set-piece goal, then it is hard to play.
"On the counter-attack they are good with their pace. 4-0 is a disastrous result for us. We were not happy at 2-0 and wanted someone up front with Chicharito, that is why we put Diafra Sakho on. We created some good situations.
"This is the worst scenario that could have happened to us but we cannot change it and we have to pick ourselves up off the floor for the next game. It is hard to talk about the pluses when you lose 4-0. Some players are coming back from injury."
West Ham have now lost 11 times on the opening weekend of a Premier League season - the worst such record in the division - while Man United have lost just one of their last 13 curtain-raisers at Old Trafford.