In an interview with Diario AS, Salah said he was "very disappointed" not to be made captain against Midtjylland in the Champions League, while the star forward also refused to rule out a move to Real Madrid or Barcelona.
Trent Alexander-Arnold was made skipper for the encounter in Denmark, but Klopp revealed he had made a mistake.
The Liverpool manager said he had discussed his decision with Salah, who has scored 16 goals in 21 games this season.
"I was captain for a long time in my career and I always thought 'what a job this is' because there are not a lot of benefits and there is a lot of work," Klopp said.
"I didn't feel, or do not feel, the importance of being captain. Before the game I did not realize how important that can be for players and I didn't realize how big a story it was for Trent.
"The rule here is we have a players' committee. The committee is Jordan Henderson, James Milner, Virgil van Dijk and Gini Wijnaldum. These are pretty much the four captains. If they all cannot play, usually it is the guy who is longest in the club. And that, how I saw it, was Trent. I don't mean youth career, but in his professional career. Then somebody told me that on that basis it should have been Divock Origi. So it was my fault.
"Afterwards I spoke to Mo about it. Then I realized it did not work out that well so I clarified it. Obviously he gave the interview. That is not a problem for me. Obviously he was disappointed. I did not do it on purpose, and if I made a mistake then it was not making Divock Origi captain that day."
Salah's interview has led to greater speculation over the Egypt international's future, although the forward is contracted at Anfield until 2023.
But Klopp cannot see why the 28-year-old would want to leave Liverpool, who host West Brom in the Premier League on Sunday.
"I don't know, we all want it and we can look for something else if you want but the only reason to leave Liverpool right now is really the weather," he said.
"What other reason could be there? This is one of the biggest clubs in the world.
"We pay good money, maybe not the most in the world, but we pay good, and we have a sensational stadium, outstanding supporters with a fanbase all over the world. Our colors are red, which is the nicest color anyway, so what is the reason? But you cannot force people to stay but that is it.
"We never did by the way, it is all about timing in the right moments, stuff like this. We have made changes to bring players in and if someone wants to leave we cannot hold them back."