"I hope I can repeat that because I know how it feels to win the Champions League," Shaqiri told Sky Sports News.
"It is really amazing and I think we can do it. We have good quality - especially with the new players that have been brought in - they have very good quality.
"I think the important thing is to be successful, and to be successful you need to win some titles and trophies and I hope we can lift some trophies this year."
The Switzerland international also rejected criticism of his performances at Stoke last season and said a big part of his decision to move to Liverpool was manager Juergen Klopp.
"When I heard the club wanted me I wanted to come because I've known him a long time. I've admired him for a long time ... He is a great person and a great character with a winning mentality and that's the most important thing," he added.
Shaqiri could make his debut against Manchester United in the International Champions Cup on Saturday.
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
