The new signing was ordered to train alone after the new Manchester United manager said he wasn't fit enough
Shaw was made to train on his own earlier this week during United's pre-season tour of the United States, with Van Gaal claiming the new signing from Southampton was not at the fitness levels he demands.
"It's something I totally agree with," Shaw said. "Playing in this formation [3-5-2] you really have to be fit. I am fit but not at [Van Gaal's] 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."
Shaw was a surprise substitute against Inter on Tuesday evening,but the left-back is confident he is now one step closer to being ready for the new Premier League season.
"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 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."
Van Gaal added: "I think he did very good tonight. 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 to play, in spite of a very heavy training session this morning."