The midfielder also says the win over Stoke has led to confidence flowing through the squad.
The Reds endured a difficult campaign last season as a poor start saw them unable to catch those ahead of them, meaning they missed out on Champions League qualification.
That of course, came after they had finished second the season before and returned to Europe’s elite competition for the 2014/15 season. To add to that disappointment, Brendan Rodgers side were also beaten in two cup semi finals last year as well.
And Lallana says they are targeting that first trophy under Rodgers and a return to the top four this season to overcome last season.
“The aim for all of us this year is to win a trophy and try to get back in the top four," he told Sky Sports.
“I feel we’ve got the starting foundation of that with a good squad and good competition for places. We’d love to get back in the top four. We had a taste of it last year and unfortunately we got knocked out in the group stages, so we want to be back in there.”
Stoke win a big confidence boost
The Reds enjoyed a winning start to their Premier League campaign with a win over Stoke City last Sunday.
It was an altogether indifferent performance from the Reds, with a number of new signings still adapting to their new sides style and learning how to play with their new teammates.
The Britannia was a big one though, and was even bigger given Liverpool were beaten 6-1 in the final game of last season, and Lallana says the it will feed a lot of confidence throughout the group.
“It will feed a lot of confidence through the group,” he added.
“Stoke’s always a difficult place to go - any team will tell you that - and any team in the top four, five will see Stoke away as one of the toughest games in the fixture list. So to go there and get three points was a massive start for us.”