Ajax won that game 1-0 but there was no first win for his new club under his management and he put that all down to missed chances, particularly in the second half after he'd told them at half time to improve their used and retention of the ball.
"We played much better in the second half and created more chances, but you have to score from those chances, and we didn't do that. It's a disappointing result," he bemoaned.
"It was our mistake to fight with Burnley, even though they have fantastic fighting spirit, You have to play with the ball against teams like Burnley.
"I don't think our confidence was very high in the first half, but I think that's normal when a club like United loses the first match and draws the second one. The pressure is higher and you have to cope with that.
"I could see in the first half that the players were very nervous to play the ball. We restored that in the second half, and maybe that will raise our confidence."
Van Gaal wouldn't comment on the two penalties United felt they should have been awarded, one for a foul on Ashley Young and the other for handball, but he said: "We had more possession of the ball than Burnley but more free kicks were awarded against us than in favour of us. I think that is remarkable."
Sean Dyche saw his side gain a first point of the season in a performance that left him proud of his team, and he was delighted about the whole experience of match day at Turf Moor.
A happy Dyche said: "Other than the performance and getting our first point, all of this with a packed Turf Moor is great to see. When I got here I don't think anyone envisaged that. That's a great journey for me and the fans, not just the players.
"I said to the players after the game, a big part of our growth is exactly that, handling all of this that comes with the Premier League, a lot more media scrutiny and TV coverage, camera angles etcetera. At Swansea we handled it and played very well and today we've handled it and played very well.
"I'm very pleased. I thought the performance was good against a very strong Manchester United side. I certainly think that’s the strongest side they have fielded this season. A lot was made of Di Maria making his debut, he’ll grow into the game of course as he’s a fine player.
“Generally I think we kept them quite quiet. Tom (Heaton) made a fantastic save in the first-half, Rooney missed a header at the back post in the second-half but other than that we were solid.
“I liked the shape of the team, I liked the energy but also the quality which we showed. I think it’s important we go into the international break after a really good performance and your first point on the board.
“And when the games come around again after taking stock of the season so far, we’ll be ready to go hard again.”