The Swiss winger completed his move to Anfield earlier this month and is hoping to achieve big things during his time with the club.
He joins a Liverpool side still reeling from their Champions League final defeat to Real Madrid, but despite having already won the competition once with Bayern Munich in 2013, Shaqiri has now set his sights on a second triumph.
"I hope I can repeat that because I know how it feels to win the Champions League," he 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 faces a tough challenge to get into the Liverpool side with Mohamed Salah, Roberto Firmino and Sadio Mane all seen as undroppable up front. but the former Stoke man says he is up for the challenge.
"It's always difficult, you always have competition everywhere in the world," he explained.
"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. And you need every player to be successful in a long season.
"The coach knows my quality and he knows I can play lots of different positions in front so I think that is going to be positive for the team and we can be more variable in the games."
Meanwhile, Shaqiri admitted that Jurgen Klopp played a huge role in convincing him to join the club.
"When I heard the club wanted me I wanted to come because I've known him [Klopp] a long time. I've admired him for a long time and I am really happy to be here," he explained.
"Jurgen Klopp is a great person and a great character with a winning mentality and that's the most important thing."
Finally, Shaqiri came in for criticism from former Stoke team-mate Charlie Adam recently, but the winger believes that the Scot's comments were unfair.
"It's totally wrong, I think," Shaqiri insisted.
"People who know me, they know who I am. Other people don't know what they are saying. I don't listen to them, I do my work. I'm really happy to do my work and I don't need to listen to these people about what they say."