Van Gaal made Shaw train on his own earlier in the week and said the teenager's fitness was not at the level he desires of his players as the start of the Premier League season looms.
Shaw, who joined United for a fee of around £27m earlier this summer, went on to make a surprise appearance in their 0-0 draw with Inter Milan in Washington on Tuesday night with Reece James injured.
And after the game, Shaw admitted the Dutchman's comments about his lack of condition were accurate, especially with the club set to line-up in a new 3-5-2 formation this season.
He said: "It's something I totally agree with. Playing in this formation you really have to be fit. I am fit but not at his high demands. I know I have got to get fitter to get up and down.
"That's something I am going to work on, and tonight in 45 minutes I felt really good, so I am looking forward to keep on progressing until the start of the season.
"I didn't come into United thinking it's going to be much harder and that's something I made a mistake on. I thought it was just going to be the same but United is the biggest club in the world and there are world-class players in training so it's something that is going to push me on.
"That's something I need to keep me pushing on and this is only going to help me in the long run.
"Pre-season you are always going to try and get your fitness up so I am not too sure but today I played 45 minutes and I felt great. I could have played on. It's a progression from the last game I played so hopefully now the main focus is getting fitter and fitter and I'll be flying by the start of the season.
"I wasn't meant to play today because me and the staff decided it would be better to push me harder in training, but I didn't have any problems and I feel good."
"he will be the England left back for ten years or more, and then you will have to thank MUFC for that." *smiles*- london saint