The French centre-back had missed Liverpool's last three matches but cut short his planned absence when he saw the extent of the club's problems, with four defenders sidelined including Joe Gomez.
It was an emotional and memorable return for Konate, who scored the fourth goal in Saturday's 4-1 comeback win over Newcastle United as the champions claimed their first Premier League victory in over a month.
"He has had a very difficult two weeks. He was planning to be back for the end of this week and it would have meant he could not play this game," Slot said.
"But when he saw the problems we had defensively, he called me early this week and said: 'I want to be back to help the team against Newcastle'.
"He came back on Wednesday and trained twice with us. Not only did he score a goal, but he played a great game and the fans were really appreciative throughout the whole game, but definitely at the end when he scored."
After scoring, Konate was mobbed by his teammates - including goalkeeper Alisson who ran the length of the pitch to celebrate with him - as the Frenchman wiped away tears and the Anfield crowd gave him a rousing standing ovation.
'Very difficult moment'
"I don't have words to describe what I feel right now because it was a very difficult moment for me and my family this past two weeks, but this is part of life. It is hard to accept that and we don't have the choice," Konate told TNT Sports.
"I know that the team had some injured players. The manager on the call said to take my time and I don't have to rush back. With this situation, it was important for me to come back and help the team."
Konate's goal came after Hugo Ekitike struck twice before half-time and Florian Wirtz also got on the scoresheet for Liverpool's first win in six Premier League games.
"Everyone was cheering for Ibou and Florian when they came in after doing TV interviews, but especially for Ibou," Slot added.
"This team has shown we are always there for each other in difficult circumstances. That's what they were for him in the last few days."
Liverpool moved provisionally up to fifth in the standings after the win, a point above Manchester United who host Fulham on Sunday.