The German international came through the ranks at Borussia Dortmund while Klopp was in charge.
And Gotze says the 50-year-old balances his jovial public image with a stern disciplinary attitude in the dressing room.
"He was my first manager, and he was the one who believed in me and gave me the chance to debut at 17 years old," Gotze told The Players Tribune.
"It's funny to see him now with Liverpool because he's such a natural guy in front of the media.
"He's so authentic and he says whatever he wants. But I think most people just see the version of him standing on the touchline.
"There's a very serious side as well. When I was 17 or 18, and not giving 100per cent in training, he would be so intimidating. He used to come running over and get right up in my face and start shouting at me.
"I can't really translate from German perfectly, but you know how he talks, with his teeth grinding: 'You have to have more passion! You have to give everything! ****! Come on!!!'
"Then after training, he would be completely calm again, and he'd take you aside and say, 'Mario, how are you? Let's talk about life. What's happening?'
"He knew how to handle me. He was an outstanding coach, but his personality was the most important thing for me as a young player."