The Red Devils salvaged a point late on at Upton Park, with Daley Blind lashing a volley past Adrian, and Allardyce lamented afterwards that his side "couldn't cope with long-ball United, it was just thump it forward and see what they could get".
Van Gaal, though, has reacted angrily to the idea that his side only played long-ball football, handing out images and statistics which contradict Allardyce's assertion, and insists United played the better possession football in Sunday's meeting.
"[We played] long balls with width to switch the play and then you see of course we play long balls, but more long balls out wide than to the strikers," began the Dutchman's staunch defence of his playing style in his pre-match press conference.
"And a ball to the forwards is mainly called long balls played. Now, because I expected this question I have made interpretation of the data of this game, and then I have to say that it's not good interpretation from Big Sam, it's not so difficult also to read.
"I'm sorry, we are playing ball possession play. After 70 minutes we don't succeed in spite of many chances in the second half, then I change my playing style and then of course with the quality of [Marouane] Fellaini we played more forward balls. We scored because of that also, so I think a very good decision of the manager."
He continued: "But, when you see overall the long ball and what is the percentage of that, then West Ham United have played 71 per cent of the long balls to the forwards and we 49%.
"So, I give you this [dossier showing long balls attempted], also you can see the blue ones are the good ones, because long balls are mostly very difficult, which is why I began with the explanation of ball possession. When you have 62% ball possession you cannot play long balls only.
"Again they did it with 71% and us 49%, and I give it to you. You can copy it, and then you go to Big Sam and maybe he can do a good interpretation."