Redknapp made the comments following the Reds’ goalless draw with Tottenham at White Hart Lane in the Premier League on Saturday afternoon.
The former England international, who played for Liverpool from 1991 to 2002 and for Spurs from 2002 to 2005, was impressed with the performance of Jurgen Klopp’s team.
However, Redknapp suggested that the Liverpool players were not showing the same commitment under Klopp’s predecessor Rodgers.
“Liverpool ran further than they have all season against Tottenham,” the Englishman wrote in The Daily Mail. “People say this is down to Jurgen Klopp and his heavy metal pressing game. Don't be fooled. Klopp is a fantastic appointment and I can't wait to see what he does but he doesn't have a magic wand.
“A team doesn't suddenly become fitter in three days. It takes hours of training to become an effective pressing team and Liverpool may not reap the benefits of Klopp's regime until next season. Look how long it's taken Mauricio Pochettino to get Tottenham playing his way.
“It was a good performance by Liverpool but they won 3-0 and 5-0 on their last two visits to Spurs. All those stats tell me is that the players weren't putting the same effort in for the previous manager or the fans, which is disappointing.”
Over the course of the 90 minutes at White Hart Lane on Saturday afternoon, Liverpool had 52% of the possession, took 12 shots of which three were on target, and earned six corners. The Reds created 10 chances, put in 18 crosses and attempted 18 dribbles.
Liverpool are 10th in the Premier League table at the moment with 13 points from nine matches, just four points behind fourth-place West Ham United.