Solanke joined Bournemouth on Friday in a reported £19million deal, having failed to make a single competitive appearance for the Reds in all competitions this season.
The former Chelsea forward arrived at Anfield at the start of 2017-18, but scored just one goal in 21 Premier League appearances last term.
And Klopp has revealed that although Liverpool were keen for Solanke to progress, they could not stand in the way of his need for regular football.
"Football is a business, but on the other side we have to care about people, their situation," Klopp said in his pre-match press conference.
"For Dominic it was absolutely right to go. It was a bit unlucky for him in the moments when there was space for him to come into the team that he had injuries. In other moments the squad was full and we had different options.
"He trained well but you cannot stay confident over that time, especially in that age group. He needed to play football.
"Bournemouth made a good offer and it's a good opportunity.
"Could there have been a moment in the next half-year where the situation could change for him? Maybe yes, but we don't want to block our young players when we see something could be better for them."
When you sign two players in one day... pic.twitter.com/64rYCzXuGC— AFC Bournemouth (@afcbournemouth) January 4, 2019
Solanke was followed to the Vitality Stadium by Nathaniel Clyne, who has also made the switch from Anfield, albeit on a six-month loan deal.
"With Clyney, having an option like him is good," Klopp added.
"When I came in, he played like what I felt was each game. He was very good and a very important part of the team in that time.
"Then he got his injury, a back problem, that nobody knew how long it would take and the team changed in that time.
"Joe [Gomez] was fit and Trent [Alexander-Arnold] came up. Having Clyney was still okay but he is at an age where he needs to play and wants to play.
"He asked if he could go and I thought about it and said yes because we have other options. You can always keep a player, but to keep him with the right shape or confidence is not always easy, and they have to play more than Clyney did."