Fabinho won five trophies with the Reds, including the Champions League in 2019 and the Premier League title a year later.
"Fab was for so long the insurance we had more or less in midfield," Klopp told the club website., external
"He always gave us the freedom to play all the fancy stuff. He was involved in that from time to time as well but loved to be the hoover for the team, loved to do all the dirty work for the team.
"So yeah, we will miss him, definitely. But again, it's like it is. Life is about changes and you obviously have to adapt to them. If you don't do that, if you stick in the past, something will hold you back - and I'm not that person.
"And yes, we will miss Fab - but Fab will be fine, we will be fine and we always will be thankful to each other. That's, for me, very important in life.
"So all the best, my friend, and hope to see you soon."