United can win their first piece of silverware since 2017 when they take on Villarreal in Gdansk on Wednesday and Greenwood said it is vital Ole Gunnar Solskjaer's team get over the line.
"To bring home a trophy is something the club needs, to bring home some silverware," Greenwood said. "We've not had any for a few years. To be a part of the team that actually does win a piece of silverware will be a good feeling.
"When you come and you're in the academy, there's pictures and photos on the walls of them back in the day winning the Champions League, the Premier Leagues, the FA Cups and that's what it's all about, really, for a football club.
"If you want to be the best football club in the world or in the country you've got to bring home the silverware and that's something United have done over many years.
"But we've maybe dropped off a little bit throughout the recent years but hopefully we can after this one, if we win against Villarreal, that can be like a little stepping stone to get us started on where we want to be."
Greenwood, 19, made a huge impact in his first full season with the first team, scoring 17 goals and earning a first call up to the England squad.
This season he has had to wait to find his best form in front of goal with eight of his 12 goals coming since mid-March but he still said he is much improved from a year ago.
"I think I've done better than last season," he added. "The performances when I weren't scoring, I still think I was playing well. I don't think I was playing poorly.
"The final end product might not have been there and obviously towards the end of the season it's kicked in, but I still feel like I've done a lot better than I had last year.
"My goals and assists might not seem like it but in my opinion -- and maybe the players around me -- I feel like I'm more of a player for the team now as well."
Since breaking into the team at such a young age, Greenwood has earned the nickname "Star Boy" from some fans.
He won't turn 20 until October and has already broken the club record for Premier League goals by a teenager, leapfrogging both Marcus Rashford and Wayne Rooney.
"I don't really mind it [the nickname] to be honest with you," he said. "I just concentrate on my football. I'm still a kid who's having fun playing for United, playing for my boyhood club with many, many great players around me."