That was the Dutch national team manager's prerogative - and loss.
Had Van Gaal been in attendance, he would have seen a tremendously-mature display of defending by 22-year-old Virgil van Dijk, so good that Hoops boss Neil Lennon believes it simply can't be overlooked.
While Ajax's rising star, Stefano Denswil, was having a night to forget - he brought down Anthony Stokes for Celtic's penalty converted by James Forrest, then deflected Beram Kayal's second-half shot which put Celtic 2-0 up - Van Dijk was delivering a master-class.
Denswil has burst to prominence since breaking into the Ajax first team this season, scoring their goal against AC Milan on matchday two, and has been tipped to be promoted into the Dutch squad ahead of next summer's World Cup finals.
But Lennon is confident that, when Van Gaal studies a DVD of this week's game, it is Van Dijk who will stand out and come into contention for Holland's World Cup warm-up games, which kick off next month.
Lennon is convinced he has snared a real bargain by signing the former Dutch Under-21 star from Groningen for £2million, and Tuesday night brought many more to the same conclusion.
Major shareholder Dermot Desmond - who, unlike Van Gaal, did choose to attend the game - must be delighted and impressed with the way the manager is reinvesting the money made from the sale of stalwarts such as Victor Wanyama, Gary Hooper and Kelvin Wilson.
Lennon said: "If Louis van Gaal was watching that, he has really got to have a look at Virgil and see if this boy is good enough.
"He was playing against a quality of opposition that Van Gaal knows well.
"Virgil is a class player, and we knew that as soon as he walked in the door.
"What's more, considering his age, he is only going to get better."
That's quite a prospect, given how well Van Dijk is already performing after taking a few months to find his feet and adapt to the more physical style of football required at his new club.
Lennon did not have any doubts he could settle and deliver, and revealed he has never had the need to take Van Dijk aside and assure him he had made the right move.
"Virgil is very confident and is in a good place at the minute," said Lennon.
"I thought he was outstanding on Tuesday night.
"There was never any panic, no matter what Ajax tried to throw at us.
"Along with Efe Ambrose, they looked great together, and I felt Efe got better in the second half."
That partnership is looking stronger by the game, defying the misgivings held by those who do not like to see two ball-playing central defenders together.
The more games Van Dijk and Ambrose help Celtic to win - especially big matches like this week's - the more they undermine that argument.
"It was massive to win on Tuesday, to beat a team like that," reflected Lennon.
"I don't care what anyone says, Ajax are not the Dutch champions for nothing.
"They drew with Milan, so we beat a very good side. The next game, in Amsterdam in two weeks, is a very big one for us.
"If we can get something there, we will be confident going into the home game against Milan.
"Unfortunately, we are going to lose Nir Biton now after his red card on Tuesday, which is a blow to us and to him.
"But we are getting reinforcements back, which is great."
Celtic will need them as the battle for qualification is only at halfway, and the toughest games have still to come as they have just one at home - against Milan on matchday five - and two away, in the Amsterdam Arena then the Nou Camp in December.
The victory over Ajax coupled with Milan and Barca drawing in the San Siro means it is still all to play for from top to bottom in Group H.
Lennon is still trying to assess how good or bad the draw between the teams first and second in the section is for Celtic.
He said: "I was pleased-ish when I heard the result from the San Siro.
"We might have preferred it if Barcelona won and were running away with the group. But I always knew this group would be tight, and that's how it is turning out."
To the relief of everyone at Celtic, because defeat on Tuesday would have cast them adrift with only a slender hope of qualifying for the Europa League.
As it is, they have climbed to third. And, if Barcelona can defeat Milan in the Nou Camp, the Hoops will have the chance to overtake the Italians when they come to Glasgow on November 26.
If Celtic can take something from Amsterdam in the meantime, that would be a pivotal night in the qualification race.
But, for now, Lennon is demanding his players re- adjust their focus to domestic matters, and that means this weekend's short trip to play Partick Thistle at Firhill.
It may be a huge climbdown from Champions League action, but the manager is happy with the way his players are fighting on both fronts.
Lennon said: "I think we are playing well domestically. But we will have to see how our walking wounded are ahead of this weekend's game.
"We are on our knees at the minute. There was a lot of fatigue in that dressing room on Tuesday night.
"So, again, I'm going to have to use the squad.
"I am not sure about Mikael Lustig's condition after he had to come off near the end when his hip seized up again.
"It might be an opportunity to give Darnell Fisher another game. We will see over the next couple of days."
Celtic are also hoping there will soon be news on the appeal lodged against skipper Brown's three-game ban for what Uefa deemed was assault on Barcelona's Neymar.
Uefa have confirmed as of yet no date has been set for the hearing, but it must happen before the Hoops play Ajax in Amsterdam in a fortnight's time.
The Hoops boss has seen the findings of Uefa's Disciplinary Committee, who imposed an extra two-game ban to the one-match automatic suspension, but insists he requires clarification.
"It is quite vague," he explained. "I'm not convinced about the wording of it.
"I think we have got a good case to appeal it."