Speaking to Sky Sports News on the back of Liverpool's Carling Cup victory at Wembley, Hamann expressed his happiness over the club putting an end to their six-year trophy drought.
However, he has called for the Reds not to get carried away with their Carling Cup celebrations, so as to focus on fighting for Champions League qualification. Hamann stated that qualifying for Europe's top club competition is vital if the club is to progress.
"To progress the club and bring the happy days and the glory days back, I probably would have taken the Champions League [qualification] over the League Cup," he shared.
"If you get in the Champions League it's extra funds, it's extra money, it's better players and I think that gives you a far better chance in the future to be successful."
The German hopes Liverpool manager Kenny Dalglish and the players, buoyed by their recent triumph, will be able to translate their cup form and bring the club back to an elite European status.
"Medium to long-term if you want to compete with the best teams,...if the team wants to progress as Comolli and Kenny said they have to get in the Champions League and they have to transform the form they showed in the Cup into the league." Hamann said.
The former Reds midfielder expressed his concern that the club could fail to attract top talents if they remain outside the top four of the Premier League.
"I slightly disagree with [director of football] Damien Comolli that they attract the best players now, you can't really compete with the top teams and attract the best players if you are not in the Champions League." he revealed.
Addressing areas that need improvement, Hamann believes that while the current team are strong in defence, the quality of passes from midfield lacks consistency.
"Their defence has been pretty solid throughout the season but going forward is where the worry is, Stewart Downing had an ok start to his career; Jordan Henderson is not a wide player really. Craig Bellamy can't play two, three games in a week." he remarked.
"So going forward that's where they need to improve if they want to challenge the top teams in England."
Liverpool return to Premier League action this Saturday when they play host to an Arsenal side on a potential resurgence.