A superb goal from Cheikhou Kouyate, the midfielder deployed in defence due to the absences of Winston Reid and James Collins, had looked like giving West Ham a deserved first Barclays Premier League win over United in seven years and at the 13th attempt.
But Daley Blind scored in stoppage time to rescue a 1-1 draw and a scarcely deserved point after a lacklustre performance from the visitors which was summed up by a second-half miss from Radamel Falcao.
United’s equaliser came after Marouane Fellaini had been sent on to cause havoc, a ‘Plan B’ after his side struggled to scrap for the ball, causing Van Gaal to call for his creative personnel to play their own game and compete for loose balls, or risk losing their places.
The Dutchman said: “We need the guts to play football along the floor. That we have done in the second half.
“With him (Fellaini) we have more power. With Adnan (Januzaj) and (Angel) Di Maria, we have more creative players. The second ball you cannot always win with these players.
“But you have to win (the ball), otherwise I have to line-up always (with) players like Fellaini.”
Allardyce said on Sky Sports: “I suppose in the end we couldn’t cope with long-ball United.
“It was just, ‘thump it forward and see what they could get’ and in the end it paid off for them.”
He added in his post-match media conference: “You (the media) might just criticise Louis van Gaal for playing long balls as much as you’ve sometimes criticised me for being direct.
“(But) it’s paid off for them, so you can’t knock it in the end.”
United finished the game with 10 men as Luke Shaw was sent off for two bookable offences.
Van Gaal insisted the second yellow card, given by referee Mark Clattenburg in the final moments for a foul on Stewart Downing, should not have been given.
The Dutchman said: “It was in front of me. The player (Downing) was jumping, but I think it was tactically not so smart of Shaw.
“I think the referee could give him a yellow card, but he doesn’t touch him.”
Van Gaal also rued the opportunity to make up ground on Manchester City, who are five points better off in second place and drew in similarly last-minute fashion with Hull on Saturday.
“It is a missed chance,” he said.
Allardyce lauded his injury-depleted side’s display as “almost the perfect performance”.
He added: “It’s a fantastic performance. Not a result we deserved or wanted, but we’re back to a level that we know we can play at.”