Shaqiri became the third signing of the Reds' summer when he completed the move from Stoke City earlier in July, but is yet to make his first appearance.
The 26-year-old won the Champions League in 2013 with the Bundesliga giants, and believes he can add to his tally with the Reds.
"I hope I can repeat that because I know how it feels to win the Champions League", Shaqiri told Sky Sports News.
"He's a very good player, but I'd be lying if I said he was right there when I saw him", he said.
"The most important thing is to go to the last limit and to try to do the small things that will help us win titles".
The Swiss worldwide hit back at the likes of his former teammate Charlie Adam, and pundit Gary Neville, both of whom criticised him heavily for his underwhelming performances as the Potters were relegated last season. "I've admired him for a long time and I am really happy to be here", he said.
Saturday's match in MI may only be a friendly, but when Manchester United and Liverpool FC get together, there is typically nothing all too friendly about it. I'm here to be successful with my team. I hope this season we can go through and improve the small things that we need. Other people don't know what they are saying. I know the league well and I have a lot of experience.
"It's always hard, you always have competition everywhere in the world", Shaqiri admitted. I have only just started with my first training session today but I didn't have a long holiday so I didn't lose too much.
"Every player wants to play on the biggest stages in football".
"We are a big team, there are big players here and everyone is going to fight for his place, but in the end we have to be successful as a team". It is important for me to work with him and with people who communicate well with good character.
"It's totally wrong, I think", Shaqiri said of questions raised about his professionalism during his time at Stoke.
Adam, meanwhile, accused his former teammate of going missing when the got tough a year ago.