The Reds have brought in the likes of Fabinho, Naby Keita, Xherdan Shaqiri and Alisson Becker during the current transfer window, but also lost a first-team regular in Can when he left for Juventus at the end of his contract.
Klopp admitted that he would have liked the club to have received some money for the Germany international, but rubbished reports that there was a rift between himself and the player after he turned down the offer of a new deal.
"We always had and still have a good relationship. I have no problem with a player leaving. The only problem I had for the club was that I wanted to get some money: 'Sign a new contract and then we'll sell you!' But that wasn't really realistic," Klopp told the Liverpool Echo.
"There was never a problem between Emre and I. Emre is 24 now. Playing in another country can be a life target: 'I've spent four years in England, now I want to go somewhere else.' Why not? He's a top player and he's gone to a top club, it's all good.
"We knew early enough that it was pretty likely he would leave and we were able to plan. There was nothing to say about it during the season. If I had said to people in March 'Yes, he will leave 100%' then immediately people would have thought he wouldn't give his all any more.
"I knew Emre would give everything. He was desperate to play in the last few games. It was only possible in the last one but not in the best shape because of the injury. Now he's in Turin, we're here and it's all good."
Liverpool will begin their new Premier League campaign at home to West Ham United on Sunday.