Mane, who was booked in the first half, was replaced before the start of the second half by his manager, despite scoring his side's second goal of the game.
But after Atletico defender Felipe's red card, Klopp stated that it was something he had to do so that Mane didn't suffer a similar fate.
"I think everyone in the stadium expected it. I thought it was the right thing to do and I hated it more than you can imagine," said Klopp.
"I was not worried that Sadio cannot handle his emotions - he was calm but the thing is the ball comes in the air for a headed challenge and the [Atletico] player goes down.
"We all saw what the Madrid players did, rolling around to try to equal the number of players again. I didn't like it but it was the right thing to do."
Whilst Mane stayed on the pitch, another one of their forwards, Roberto Firmino, didn't.
The Brazilian, who came on at half time, had to be replaced himself in the 78th minute, with what Klopp confirmed to be a hamstring injury.
But the German boss says that was one of the only downsides of the evening after his side secured qualification for the knockout stage.
"If Firmino hadn't gone off with a hamstring injury it would have been much better," added Klopp.
"Pretty much from all our points of view, it was a good performance. I wouldn't have expected that when I saw the draw. No one would have expected that so doing it was pretty special.
"For tonight, job done, two games to go and we will try everything to win those too."