The Reds made an unexpected charge to the final of the competition last season before falling to Real Madrid in Kiev, but since then they have significantly strengthened their squad with the arrivals of Shaqiri, Fabinho, Naby Keita and Alisson Becker.
Shaqiri already has one Champions League winners' medal to his name having been part of the Bayern Munich squad that lifted the trophy in 2013, and he is confident that Liverpool can be a force on the European stage once again next season.
"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'm looking forward to the new season and I hope we can finally win titles.
"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."
Shaqiri trained with his new teammates for the first time on Wednesday and could make his debut for the club against Manchester United in the International Champions Cup on Saturday.