Diagrams in the pamphlet claim to show United's passes went sideways or diagonally, rather than forward.
'When you have 60 per cent ball possession do you think that you can do that with long balls?' Van Gaal asked.
'Yeah, long balls, in the width, to switch the play. You have to look at the data and then you will see that we did play long balls, but long balls wide, rather than to the striker. A ball to the forward striker is mainly caused long-ball play. It is not so difficult also to read that.
'You have to see the data and put the data in the right context I believe.'
Van Gaal talks regularly about the fact that he wants his teams to play attractive football.
He was clearly, therefore, annoyed at Allardyce's comments and he had the pamphlet on his desk waiting when he fielded the first question about the West Ham boss' jibe.
'Because I expected this question, I have made an interpretation of the data for this game and then I have to say that it is not a good interpretation from Big Sam,' said Van Gaal.
Speaking after the match, Hammers boss Allardyce said:''In the end we couldn't cope with Long-ball United. It's not how you normally see United play, but it got them a goal in the end.
'You might just criticise Louis van Gaal for playing long balls as much as I'm sometimes criticised for being direct. In the end it's paid off for them so you can't knock it.'
The Dutchman however, insisted his team only started launching balls forward after 6ft 4in Marouane Fellaini came on in the 76th minute of the draw in east London.
'I am sorry, but we are playing ball possession play and after 70 minutes we did not succeed, in spite of many chances in the second half, then I changed my playing style.
'Then, of course, with the quality of Fellaini we played more forward balls and we scored from that, so I think it was a very good decision of the manager.
'But, when you see overall the long ball, and what is the percentage of that, then West Ham have played 71 per cent of the long balls to the forwards and we 49.'
After reeling off the statistics, Van Gaal rose from his chair and handed the pamphlet to the reporter who asked the question about Allardyce.
The United boss then asked them to analyse the last three pages, which contained diagrams which contained coloured arrows pointing in the direction of both team's passes.
'I give you this and you can see that the blue ones are the good ones because long balls are also very difficult, which is why I began with the explanation of ball possession,' the 63-year-old said.
'When you have 60 per cent ball possession you cannot play long balls. So again, they did it 71 (per cent) and we 49, and I give it to you, you can copy it and then maybe you can go to Big Sam and he will get a good interpretation.'
Van Gaal's delivery was calm and he only came to the brink of losing his patience once.
'What do you think?' Van Gaal snapped when first asked about Allardyce's comments, before he regained composure and reeled off his speech on why he thought the former Blackburn manager was wrong.
Van Gaal's overall tactics have come in for criticism this season. United may be fourth in the Barclays Premier League, but the team lacks the energy, dynamism and flair of the Sir Alex Ferguson era.
'I think we have played attractive games and less attractive games,' Van Gaal said. 'You can always improve, you can never have a perfect match.
'I am happy with the results, but I also think we can improve which is also the process. We have talked about already from my first day, but we have to improve.'
