The left back has won three trophies at Old Trafford since arriving from Southampton in 2014, but the club are without success now since 2017.
"How big the club is and how successful it's been in the past, I think [is what] inspires all of us, especially the ones that are there now," Shaw told the United website.
"We've seen how good and how great it is when the club's winning trophies and we obviously want to get to that stage and inspire young people, like I once was, watching United win a trophy.
"The squad, the group we have, is amazing. Everyone gets on great and we all love each other and we all want to push each other towards that goal of winning trophies."