The 26-year-old completed a hasty move to the Bundesliga side last Friday, which caught many people by surprise.
Speaking in a pre-match press conference on the same day, Klopp, who is said to have a 'close relationship' with the Ghanaian star, joked: "I'm really surprised.
"I sent him a text message saying 'Why Schalke?!' with eight question marks, but I didn't hear back from him. He was a good lad, up until this morning."
However, Boateng has not taken kindly to the comments.
"Many people thought it was funny, but I didn't," he told Bild.
"Even if Kloppo and I have a good relationship, he's not going to hear me say a bad word about him, but this press conference surprised me."
Boateng cost the Miners €15m (£12.6m) from AC Milan.