Hamann wrote in the Sunday Times that the decision to give the German a four-year extension after only one full season at the club was "madness".
"I found it strange," he told the BBC.
"You don't get stability from a six-year contract - you get it from good work in the transfer market."
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Liverpool - who lost 2-0 to Hull on Saturday - are yet to earn a league win in 2017 and were knocked out of the EFL Cup by Southampton and the FA Cup by Wolves in January.
After the Hull defeat Klopp said the performance was "not acceptable" and his team "needs to wake up".
Since taking over from Brendan Rodgers in October 2015, Klopp has led Liverpool to an eighth-placed league finish and to the final of the League Cup and Europa League, where the Reds lost to Manchester City and Sevilla respectively.
"He had an impact and has improved some players but if you look at the pure facts, the points average didn't improve dramatically from Brendan Rodgers' time," Hamann told Match of the Day 2 Extra.
"They have lost two finals - both they could or should have won - and then the club make a decision with their heart and not their head and extend the contract."
Liverpool were Chelsea's closest rivals at the top of the Premier League on 4 January - trailing by five points - but are now fifth, 13 points behind the leaders.
"I hope he is there for six years, that means the club will have been successful," Hamann said.
"But if you look at the table, they were one of the favourites for the title six or eight weeks ago and now there is a big question mark whether they will finish in the top four.
"In recent years whenever the chips have been down the team have failed and that hasn't changed with Klopp.
"Whether Klopp can change it with this team, or another, I am not sure, but something has to change because the way the team is going in recent years is not good enough."
Liverpool acted with their "hearts and not their heads" when they offered manager Jurgen Klopp a six-year contract in the summer, according to former Reds midfielder Dietmar Hamann.