The new captain also says the Champions League is the main aim as it's where the club belongs.
The Reds were defeated in both domestic cup semi finals last year, with a disappointing display in two legs against Chelsea in the Capital One Cup followed by an even poorer showing in the FA Cup semi final against Aston Villa.
Both of those semi finals were very tangible opportunities for Brendan Rodgers and his side to win the first trophy of his reign and Henderson says he is looking to secure that first triumph next season.
"I think definitely winning something, winning a trophy," he told liverpoolfc.com when asked what his aims for next season are.
"It would be big for the players, it would be big for the club and obviously for the fans, I think that's a big aim for us this season.”
Champions League football where Liverpool belong
While a trophy next season would be nice for both the fans and Rodgers, it is undeniable that the main aim is qualifying for the Champions League once again.
The Reds of course participated in the competition last season after finishing in second the year before, but it was a short lived run as they failed to find a way out of a relatively winnable group, aside from eventual winners Real Madrid.
It will be a tough challenge to make it into that top four next season though, although Henderson insists that’s the level Liverpool football club deserves to be playing at.
"Also getting back in the top-four and the Champions League,” he added.
“This football club deserves to be playing in the Champions League every year so that will be a big objective, and then once you are in and around that top four you never know what can happen.”