Lovren spent six years at the Reds before moving to Zent St. Petersburg in July.
The 31-year-old is an extremely passionate person, and admits he had some clashes with Klopp.
"We had some nice conversations in his office. It also got very loud, but always with respect," he told German magazine Kicker.
"I had the feeling that I was no longer counted on in Liverpool. But I don't want to be a substitute; I want to play football.
"Playing because others are injured – that's exactly what I didn't want anymore.
"I want to be important to a team, and that's me here at Zenit.
"I actually wanted to leave in the summer of 2019, but that didn't work out in the end.
"Fortunately, that's how I left as a master."