The Argentine managed the playmaker during his time with the Saints, before leaving for Spurs - while Lallana left for Anfield.
Adapting to a new environment, he says, is never easy, especially with former Liverpool boss Brendan Rodgers under pressure at the time.
The Tottenham boss told reporters: "Liverpool is different to Southampton. A different environment and a different club. You always need to settle into a new club to perform well.
"[Dejan] Lovren, [Rickie] Lambert, Lallana and now Nathaniel Clyne, it was a very difficult period for them when they arrived, with Brendan Rodgers not in a good position. Now he has left the club. That’s never easy.
"They are still great players. You always need time to settle into a new style, club and city. It’s not easy."
A big season for the 27-year-old?
The problem for Lallana, however, is that time is running out if he wants to become a big player at Liverpool.
The former Southampton man is often praised for his trickery but, in truth, thousands of players can produce the odd trick. Lallana has so far proved too much of a soft touch and, unfortunately, is far too reminiscent of Joe Cole - while he isn't young by modern footballing standards.
His time under Klopp, perhaps starting against Tottenham later today, will make or break his Liverpool career. The German may love his creativity... or decide he doesn't have the intensity to fit into his 'heavy metal football' system.