Klopp joined the Reds in October 2015 after seven successful years with the Bundesliga club - a transfer that Watzke said made him cry “real tears".
“'You know it too: it's better to leave now after seven years,' Jürgen said," Watzke writes in his new book 'REAL LOVE. A life with BVB', serialised by Bild.
"We did not try to change his mind anymore. But that was maybe a mistake. Perhaps it would have been better if we had exchanged the entire team – not the coach.
“Because I knew that, we would never get back such a coach. When I said goodbye, real tears came.
“Such a relationship, as I had with Jürgen over seven years at BVB, that did not exist before. And such a relationship will probably never happen again.
“This is a bit like when the children move out. You also know that it will happen at some point, but you still miss them."
Klopp has led Liverpool to incredible success, winning the Champions League last season.
"The most important thing in our relationship was and is that we can rely on each other blindly," Watzke added.
“Jürgen never lied to me. He is always honest, even in the job. And I never lied to him.
“Even in the most difficult phase, in the season of separation, when we crashed to the last place sometime shortly before the separation in the Bundesliga, that was the case."