Shaw featured in the draw with Inter Milan in the US.
"It was great, I think it was really important to get that first 45 minutes under my belt [against LA Galaxy] because I had only trained for three days," Shaw told manutd.com.
"To play my first game in front of that huge crowd was something different for me. The fans were amazing. Even though we're here in America, there are so many United fans everywhere.
"That's something I've noticed. That's obviously true in England too but in America and I'm sure around the world there are many more and that's something that makes me realise just how big the club is."