The England international was signed under Klopp’s predecessor Brendan Rodgers in a £25m deal from their Premier League rivals Southampton in 2014.
Lallana struggled in his first 18 months at Anfield before Klopp was appointed as Liverpool’s new manager in October 2015.
The 28-year-old scored seven times in 49 appearances in all competitions last season but the Reds midfielder has started this season in impressive style, netting three goals in six Premier League starts.
Speaking on Sky Sports ahead of Liverpool’s home clash against Manchester United, Carragher hailed Lallana’s development under the former Borussia Dortmund manager since his appointment 12 months ago.
“Lallana has been a massive success story for Jurgen Klopp. I christened him ‘the nearly man’. Neat and tidy but couldn’t really hurt the opposition,” Carragher told Sky Sports.
“I think he’s brought that into his game now with a lot of goals this season. When you think of pressing and how much distance needs to be covered in a game with high intensity, I think he’s one of the three or four most important players in this Liverpool team in Jurgen Klopp’s eyes.”
Lallana scored 12 goals in 68 appearances in the Premier League for Southampton before his big-money move to Liverpool in 2014.
The Reds star has scored against Arsenal, Leicester City and Hull City in the 2016-17 Premier League season so far.
Liverpool will host West Bromwich Albion in their next Premier League game at Anfield on Saturday evening.
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