Kenny Dalglish's side will take a 1-0 lead into the second leg of their Carling Cup semi-final tie with Manchester City, but Hamann has stated that finishing in the top four of the league is more crucial than securing a cup.
"Liverpool have not won a trophy for a number of years and it's very important to get that first trophy with a new group of players," the German told talkSPORT.
"But finishing in the top four might be even more important. If they want to compete with the big teams they need the income the Champions League brings and to miss out for a second successive year would not be good for them."
Hamann, 38, spent seven years at Anfield, making 191 league appearances for the club.