On the eve of the 5-3 penalty shootout win, Van Gaal criticised Shaw for turning up to pre-season out of shape.
The Manchester United manager created a special individual training plan for the player to get him up to speed for the new season.
That plan included an intense fitness session on the morning of the International Champions Cup game in Washington DC.
Van Gaal had planned to bring Reece James on as a second-half substitute, but he introduced Shaw instead after the United youth product suffered an injury just before kick-off.
Despite a lack of preparation, Shaw performed well off the bench, much to Van Gaal's happiness.
"I think he did very good tonight," Van Gaal said.
"He's working very hard
He was lucky today because I was going to play our friend Reece James but he was a little bit injured.
"And so I asked (Shaw), in spite of a very heavy training session this morning, (to play)."
Van Gaal maintained his unbeaten record as United boss, but his latest victory came courtesy of a penalty shootout following a 0-0 draw after 90 minutes with Inter.
Ashley Young, Shinji Kagawa, Tom Cleverley, Darren Fletcher and Javier Hernandez all scored from the spot to give United a 5-3 victory.
The players showed supreme confidence in dispatching the penalties - a complete contrast to United's last penalty shootout, which they lost 2-1 to Sunderland under David Moyes.
Van Gaal, who masterminded a penalty victory over Costa Rica in the World Cup, made his players practice penalties extensively on the eve of the match.
The Dutchman hailed the win as the best of United's three-match old tour, but despite an impressive showing from his back line, he admitted he is looking to sign at least one defender before the transfer window closes.
"I am very pleased
I think we played by far the best match (of the tour)," said Van Gaal, who criticised his players for their poor ball retention in the 3-2 win over Roma last week.
"We deserved the victory, I think.
"I am pleased not only because of the way we kept possession, but because of the quality of the opponent.
"The had only one shot on our goal and that was given by the referee (a free-kick).
"We also created six or seven chances so then it is seven against one."
Despite seeing target Stefan de Vrij sign for Lazio, Van Gaal has not lost enthusiasm in his pursuit of a new centre-back.
United are finding it hard to persuade Borussia Dortmund to part with Mats Hummels while a move for Arsenal's Thomas Vermaelen is yet to materialise.
The United boss is still hoping new arrivals will come though.
"I am looking at the defenders we have first," Van Gaal said.
"And when you see our three matches, we are doing well I think but it is right that we are looking for defenders because a lot of defenders have gone.
"We have to replace them but I like also like Michael Keane and Tyler Blackett.
"We have to wait and see if we can do that in more matches.
"I think the Premier League is another taste."
The first half at the FedEx Field - the home of NFL side the Washington Redskins - was a dull affair, with only Phil Jones testing Inter goalkeeper Samir Handanovic.
But United perked up after the break after the manager made eight changes.
As well as Shaw, Wilfried Zaha also impressed off the bench
The former Crystal Palace man was the only player not to feature on the tour until Tuesday night's game.
Zaha went on a couple of mazy runs into the Inter box and could have had a penalty after he went down in the box under pressure.
Van Gaal was impressed with Zaha, but he admits the England international will have to fight hard to feature on a regular basis.
He said: "I was pleased with his performance but we have to see and wait and he has a lot of competition with the other strikers."
Source : PA
Source: PA