The centre-back looked in severe discomfort when he left the field against the Seagulls, having suffered an apparent shoulder injury, and he used his shirt as a sling as he walked off the pitch during the league affair.
Slot was unable to confirm the extent of the injury when he was questioned after the match, but the Liverpool head coach said that Konate could not continue due to the pain that he was in.
"He had a lot of pain during half-time so then you have to make the change. The good thing is we have two very good replacements in Joe Gomez and Jarell Quansah. I chose Joe today because Jarell was really tired and he proved I was right because he was outstanding in the second half," Slot told Sky Sports News after the clash.
"He [Gomez] had a very good performance without the ball. He constantly stepped into midfield to win the ball, winning the duels, and when he had to defend he did very well. Very good second half."
Konate suffered an apparent shoulder injury vs. Brighton
Liverpool trailed 1-0 at Anfield, with Ferdi Kadioglu making the breakthrough in the 14th minute of the contest, but Cody Gakpo levelled the scores in the 69th minute before Mohamed Salah won it for the Reds three minutes later.
It proved to be an incredibly positive afternoon for the Merseyside giants, as Arsenal and Manchester City both lost, and Liverpool are now top of the Premier League table, two points ahead of the Citizens.
The victory has come at a cost, though, with Konate seemingly facing a spell on the sidelines.
Liverpool will be back in action on Tuesday evening again Bayer Leverkusen in the Champions League, before welcoming Aston Villa to Anfield in the Premier League next weekend, and Konate could be absent for both of those fixtures.
Slot admits Liverpool were "outplayed" in first half against Brighton
Slot said that his side were second-best in the first half against Brighton but praised the Reds for their display in the second period.
"We needed another second-half performance but because we were outplayed in the first half. They were better on the ball, more aggressive without the ball. Then, everything changed in the second half because it was completely the opposite," he said.
"Our attackers scored the goals but the main difference was we were better positioned and we had the ball a lot more. Without the ball they made problems for us but in the second half we just kept running.
"It's more if you play against Arsenal in their stadium and you can get a draw away from home. Brighton are a very strong team as well, they have shown this season. If you face a team like this and are 1-0 down and can come back to a 2-1 win which in my opinion was deserved that gives me a lot of confidence. More than the position we are in."
Liverpool have now won eight of their opening 10 Premier League matches of the season under Slot, which is the most ever by a head coach of the Merseyside club in his first 10 top-flight games at the helm.