And Bilic's side so nearly added another famous scalp to their collection this season after wins on the road at Arsenal, Liverpool and Manchester City.
But both Mauro Zarate and Winston Reid hit the post while Victor Moses wasted a one-on-one when clean through.
Zarate should also have scored after being set up by Andy Carroll in what was the most clear cut chance of the game in the second half.
'We are the attacking team not West Ham'
After the game, though, van Gaal - who is under intense pressure from fans over Manchester United's lack of goals - insisted his side deserved to win.
"I don't understand why the fans shout 'attack, attack' because we are the attacking team and not West Ham United," he told the press after the game, as reported by the Guardian.
"And that is not only today, that is in every game because we are always more dominating than our opponent."
Bilic bites back
But Bilic has now hit back at van Gaal's claims on the club's official website.
“We didn’t only defend, on the contrary, we created enough chances against them and it was a very good day for us," Bilic told whufc.com.
“But you never know in football.
"If we had scored then we might have lost 2-1!”
Louis the second
It's not the first time van Gaal has been irked after a game against West Ham.
Back in February, the Dutchman let rip at then Hammers boss Sam Allardyce after he labelled United long-ball merchants following their 1-1 draw at Upton Park.
The Dutchman was far from impressed and at the press conference for the next game produced a sheet of statistics from the West Ham match and handed it to reporters, claiming they showed it was in fact the Hammers who played more long balls - as reported by the Mirror at the time.